The spin, the nutation, and the precession of the Earth's axis revisited from a (numerical) mechanics perspective (Englisch)

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Modeling the motion of the Earth's axis, i.e ., its spin, nutation and its precession, is a prime example of our ongoing effort to simulate the behavior of complex mechanical systems. In fact, models of increasing complexity of this motion have been presented for more than 400 years leading to an increasingly accurate description. The objective of this paper is twofold namely, first, to provide a review of these efforts and, second, to provide an improved analysis, if possible, based on today's numerical possibilities. Newton himself treated the problem of the precession of the Earth, a.k.a. the precession of the equinoxes, in Liber III, Propositio XXXIX of his Principia . He decomposed the duration of the full precession into a part due to the Sun and another part due to the Moon, which would lead to a total duration of 25,918 years. This agrees fairly well with the experimentally observed value. However, Newton does not really provide a concise rational derivation of his result. This task was left to Chandrasekhar in Chapter 26 of his annotations to Newton's book . He follows an approach suggested by Scarborough starting from Euler's equations for the gyroscope and by calculating the torques due to the Sun and to the Moon on a tilted spheroidal Earth. These differential equations can be solved approximately in an analytic fashion, yielding something close to Newton's more or less fortuitous result. However, the equations can also be treated more properly in a numerical fashion by using a Runge‐Kutta approach allowing for a study of their general non‐linear behavior. This paper will show how and discuss the outcome of the numerical solution. A comparison to actual measurements will also be attempted. When solving the Euler equations for the aforementioned case numerically it shows that besides the precessional movement of the Earth's axis there is also a nutational one present. However, as we shall show, if Scarborough's procedure is followed, the period of this nutation turns out to be roughly half a year with a very small amplitude whereas the observed (main) nutational period is much longer, namely roughly nineteen years, and much more intense amplitude‐wise. The reason for this discrepancy is based on the assumption that the torques of both the Sun and the Moon are due to gravitational actions within the equinoctial plane. Whilst this is true for the Sun, the revolution of the Moon around the Earth occurs in a plane, which is inclined by roughly 5° w.r.t. the equinoctial. Moreover, this plane rotates such that the ascending and descending nodes of the moon precede with a period of roughly 18 years. If all of this is taken into account the analytically predicted nutation period will be of the order of the observed value . As in the case of the precession we will provide a more stringent analysis based on a numerical solution of the Euler equations, which leads beyond the results presented in Sect.12.10 of . Modeling the motion of the Earth's axis, i.e ., its spin, nutation and its precession, is a prime example of our ongoing effort to simulate the behavior of complex mechanical systems. In fact, models of increasing complexity of this motion have been presented for more than 400 years leading to an increasingly accurate description. The objective of this paper is twofold namely, first, to provide a review of these efforts and, second, to provide an improved analysis, if possible, based on today's numerical possibilities. Newton himself treated the problem of the precession of the Earth, a.k.a. the precession of the equinoxes, in Liber III, Propositio XXXIX of his Principia . He decomposed the duration of the full precession into a part due to the Sun and another part due to the Moon, which would lead to a total duration of 25,918 years. This agrees fairly well with the experimentally observed value. However, Newton does not really provide a concise rational derivation of his result. This task was left to Chandrasekhar in Chapter 26 of his annotations to Newton's book . He follows an approach suggested by Scarborough starting from Euler's equations for the gyroscope and by calculating the torques due to the Sun and to the Moon on a tilted spheroidal Earth. These differential equations can be solved approximately in an analytic fashion, yielding something close to Newton's more or less fortuitous result. However, the equations can also be treated more properly in a numerical fashion by using a Runge‐Kutta approach allowing for a study of their general non‐linear behavior. This paper will show how and discuss the outcome of the numerical solution. A comparison to actual measurements will also be attempted. When solving the Euler equations for the aforementioned case numerically it shows that besides the precessional movement of the Earth's axis there is also a nutational one present. However, as we shall show, if Scarborough's procedure is followed, the period of this nutation turns out to be roughly half a year with a very small amplitude whereas the observed (main) nutational period is much longer, namely roughly nineteen years, and much more intense amplitude‐wise. The reason for this discrepancy is based on the assumption that the torques of both the Sun and the Moon are due to gravitational actions within the equinoctial plane. Whilst this is true for the Sun, the revolution of the Moon around the Earth occurs in a plane, which is inclined by roughly 5° w.r.t. the equinoctial. Moreover, this plane rotates such that the ascending and descending nodes of the moon precede with a period of roughly 18 years. If all of this is taken into account the analytically predicted nutation period will be of the order of the observed value . As in the case of the precession we will provide a more stringent analysis based on a numerical solution of the Euler equations, which leads beyond the results presented in Sect.12.10 of .

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Brod, K. / Plaschko, P. / Bruhns, O. / Lehmann, Th / Zyczkowski | 1996
44
Introduction to Mechanics and Symmetry
Marsden, J.E. / Ratiu, T.S. / Maisser | 1996
44
A generalization of the Helmholtz conditions for the existence of a first-order Lagrangian using nonholonomic velocitiesThis work has been supported by the German Science Foundation (DFG) under contract No. Ma 1505-26
Jungnickel, U. / Kielau, G. / Maißer, P. / Müller, A. | 2009
44
A Arammatical Approach to Graph Drawing
Brandenburg, F.J. | 1996
44
Applied and Theoretical Problems in Graph Drawings
| 1996
45
A Bifurcation Theory for a Nonconvex Unilateral Laminated Plate Problem Formulated as a Hemivariational Inequality Involving a Potential Operator
Goeleven, D. | 1997
45
Mass Conservation in a Dynamic Numerical Method for a Model of the Urine Concentrating Mechanism
Pitman, E.B. / Layton, H.E. | 1996
45
Transient Pressure Variation of a Fluid in a Gravity-Free Environment MA
Schieber, D. | 1996
45
Stokes Phenomenon for High Order Differential Equations
Wood, A. | 1996
45
Transient Pressure Variation of a Fluid in a Gravity-Free Environment
Schieber, D. | 1996
45
Applications of spline functions to dynamics problems for flexible rod-cable structures
Bezverkhyi, O.I. | 1996
45
How to Write Symbolic-Numeric Programs in A# Without Interprocess Communication
Dooley, S.S. | 1996
45
Book Review: V.I. Feodosiev, Advanced Stress and Stability Analysis.
Altenbach, J. | 2006
45
Minisymposium 3 - Combustion - Transient numerical simulation of combustion in inert porous media
Knabner, P. / Neef, M.J.de / Summ, G. | 1999
45
Book Review: Michel Favre‐Marinet and Sedat Tardu, Convective Heat Transfer – Solved Problems
| 2011
46
Chaotic Behaviour in Nonlinear Oscillators
Iyengar, R.N. | 1993
46
Topology optimization of slightly compressible fluids
Evgrafov, A. | 2006
46
Reflection and transmission of water waves in a two‐layer fluid flowing through a channel with undulating bed
| 2011
47
Edge Crossings in Layered Drawings of Graphs
Eades, P. | 1996
47
On Transformations and Perturbations of Orthogonal r-Frames
Sherif, N. | 1993
47
On a posteriori error indication based on finite differences in triangular grids
Sonar, Th / Warnecke, G. | 1998
47
A simple model for a vibrating element density meter in two phase flow
Billingham, J. | 1996
48
Solution of the Lyapunov matrix equation for a system with a time-dependent stiffness matrix
Pommer, C. / Kliem, W. | 2004
49
On Interface Edge Singularities in Layered Composites
Chimani, C.M. / Bohm, H.J. / Runmerstorfer, F.G. | 1998
49
Eröffnung des Minisymposiums "In Memoriam Eric Reissner" am Montag, dem 24. März 1997 auf der Jahrestagung der GAMM 1997 in Regensburg
Stein, E. | 2000
49
Integrable Discrete Dynamics and Fibonacci Sequences
Blackmore, D. / Kappraff, J. | 1996
49
Delta wave formation and vacuum state in vanishing pressure limit for system of conservation laws to relativistic fluid dynamics
Yin, Gan / Sheng, Wancheng | 2015
49
Minisymposium 4 - Konzepte numerischer Software - Abstract data structures for a finite element package: Design principles of ALBERT
Schmidt, A. / Siebert, K.G. | 1999
49
The interaction of a moving fluid-fluid interface with a flat plate
Billingham, J. / King, A.C. | 1996
49
Numerical Simulation of Pulsatile Convective Diffusion in Large Arteries
Rappitsch, G. / Perktold, K. | 1996
49
High Performance Computing and Numerical Simulation of Flames
Douglas, C.C. / Ern, A. / Smooke, M.D. | 1996
50
DNA elastic nonlinearities as multiple smooth combinations of soft and hard linear springs
Xiao, H. | 2013
51
Modelling of Polymer Crystallization in Temperature Fields SHORT COMMUNICATIONS
Burger, M. / Capasso, V. / Eder, G. | 2002
51
Fundamental solutions of partial difference equations
Veit, J. | 2003
51
On the domain of validity of the near-parallel combined stability analysis for the 2D intermediate and far bluff body wake
Tordella, D. / Belan, M. | 2005
51
Influence of friction on critical loads for structures on elastic foundation
Muc, A. | 1988
51
Crossing Regular Drawing of Graphs
Harborth, H. / Mengersen, I. | 1996
51
Numerische Integration von hypersingulären Integralen granzzahliger Ordnung
Strauss, R. | 1998
51
On Damage Effect Tensors of Anisotropic Solids
Lam, K.Y. / Zhang, J.M. | 1995
51
High Index Differential-Algebraic Equations for Control Problems in Mechanics
Blajer, W. | 1996
52
Linear plane wave propagation and normal transmission and reflection at discontinuity surfaces in second gradient 3D continua
dell'Isola, F. / Madeo, A. / Placidi, L. | 2012
52
Book Review: Leonid I. Zaichik, Vladimir M. Alipchenkov, Emmanuil G. Sinaiski, Particles in Turbulent Flows
Jeong, H.-Y. / Moore, I.D. | 2010
53
On the Determination of the Solutions for the Kinetic State of Single-Freedom Multi-Body Systems with Friction
Klepp, H.J. | 1997
53
Efficient Computational Algorithms for Kidney Modeling
Tewarson, R.P. / Moon, I.H. | 1996
53
Minisymposium 5 - Robust Design - Robust Design
Eschenauer, H.A. / Marti, K. | 1999
53
Einfluss von Eigenspannungen auf das Steifigkeitsverhalten von Verbundwerkstoffen
Bode, J. / Middendorf, P. / Weber, T. | 1996
53
A Unified Representation of Variational Principles in Non-Linear Elasticity
Bufler, H. | 2000
53
Stability of new implicit iteration procedures for a class of nonlinear set-valued mixed variational inequalities
Fang, Y.-p. / Deng, C.-x. | 2004
53
COX - C with Operator eXtension
Lindemann, R. / Rump, S.M. | 1996
53
Asymptotic Waves in the Hydrodynamical Model of Semiconductors Based on Extended Thermodynamics
Romano, V. / Torrisi, M. | 2001
53
The influence of hydrostatic stress on the frequency equation of flexural waves in a magnetoelastic transversly isotropic circular cylinder
Abd‐alla, Abo‐el‐nour N / Raizah, Aishah / Placidi, Luca | 2016
53
Residual strength analysis of damaged laminated composites
Gädke, M. / Tang, X. | 1998
53
On some constitutive equations for micropolar plates
Turkyilmazoglu, M. | 2010
53
Finite Difference Schemes for a Non-linear Heat Equation with Functional Dependence
Leszczynski, H. | 1999
53
On a Description of Long-time Behaviour of Dissipative Perturbations of Infinite Dimensional Hamiltonian Systems
Chueshov, I. | 1996
54
Nonlinear Oscillations: One Hundered Years after Liapunov and Poincaré
Mawhin, J. | 1993
54
A finite element method for the resolution of the Reduced Navier-Stokes-Prandtl equations
Barrenechea, G.R. / Chouly, F. | 2009
55
Knowledge Through Images for the Cultural Heritage Protection
| 1996
55
Minisymposium 5 - Robust Design - Response surfaces and robust design
Schoofs, A.J.G. | 1999
55
Art-Work Image Processing and Transmission
Abrardo, A. / Alparone, L. / Cappellini, V. | 1996
55
Über einige bemerkenswerte Eigenschaften schleichender Strömungsfelder in Schneckenmaschinen
Böhme, G. | 1996
55
Approximate Solutions and Numerical Errors of a First-Order Differential Equation Related to Bifurcations of Several Maps
Klepp, H.J. | 1993
57
Scientific programming language concepts
Ullrich, C.P. | 1996
57
Parameteridentifikation für elastisch-plastische Stoffgesetze an Proben mit inhomogener Spannungsverteilung
Bohnsack, E. | 1996
57
On Cosserat–Bingham fluids
Shelukhin, V.V. / Ružička, M. | 2013
57
On the Hydromagnetic Flow between Two Rotating Eccentric Cylinders
Kandaswamy, P. / Murugesan, K. / Debnath, L. | 1994
57
Direct and inverse acoustic problems in a shallow ocean
Gilbert, R.P. / Lin, Z. | 1996
57
Computer Assisted Study of Strange Attractors of the Kuramoto-Sivashinsky Equation
Papageorgiou, D.T. / Smyrlis, Y.S. | 1996
57
Predicted stresses in die‐carrier assemblies in “stretchable” electronics: is there an incentive for using a compliant bond?
| 2011
57
New Simple Criteria for the Jacobi, Gauss-Seidel, and SOR Iterations
Huang, T.-Z. | 1996
57
Modelling of Matrix Cracking in Composite Laminates
Gudmundson, P. / Adolfsson, E. | 1998
57
New Simple Criteria for the Jacobi, Gauss-Seidel and SOR Iterations SC
Huang, T.-Z. | 1996
58
Three-Dimensional Viscous Flow and Heat Transfer along a Porous Plate
Singh, K.D. | 1993
58
Fundamental solutions of equilibrium equations for gradient model describing the deformation of two-component elastic composites
Kabysh, Yu | 2008
59
Application of Point Methods to Large Scale Optimization Problems
| 1996
59
The Use of Defect Correction for the Solution of Parabolic Singular Perturbation Problems
Hemker, P.W. / Shishkin, G.I. / Shishkina, L.P. | 1997
59
Inverted Pendulum Parametrically Driven by Dichotomous Noise SC
Schiehle, K. / Behn, U. | 1996
59
Structured Interior Point SQP Methods in Optimal Control
Steinbach, M.C. | 1996
59
Minisymposium 5 - Robust Design - Opimal design of trusses by using stochastic linear programming techniques
Marti, K. / Stöckl, G. | 1999
59
Inverted Pendulum Parametrically Driven by Dichotomous Noise
Schiehle, K. / Behn, U. | 1996
59
On Spatial Variational Problems in the Gas Lubrication Theory
Boldyrev, Yu / Lupuleac, S. / Shinder, J. | 1996
59
The arithmetic mean property for rotational symmetrical inclusions with rotational symmetrical eigenstrains
Xu, B.X. / Wang, M.Z. | 2007
60
The generalization of Holditch theorem for closed space curves
Düldül, M. / Kuruoglu, N. / Tutar, A. | 2004
61
Structure of a C++ Library for Parallel Accurate Linear Algebra
Gudenberg, J.Wolff von | 1996
61
Influence of the Integration Steps on the Results of Numerical Simulations for a System with Friction
Klepp, H.J. | 1995
61
Stokes Flow Past a Non-Newtonian Fluid Spheroid
Ramkissoon, K. | 1998
61
The Riccati Method for Sound Propagation in Ocean
Lu, Y.Y. / McLaughlin, J.R. | 1996
61
Three dimensional Stress Analysis of Composite Plates and Shells for Improved Failure Prediction
Rolfes, R. / Rohwer, K. | 1998
61
The Fully Plastic Rotating Solid Disk of Variable Thickness
Güven, U. | 1994
61
Study of the effect of viscosity and homogeneous horizontal magnetic field on Rayleigh-Taylor instability
Hoshoudy, G.A. / El-Ansary, N.F. | 2003
61
Asymptotic Expansions of Canards with Poles. Application to the Stationary Unidimensional Schrödinger Equation
Benoît, E. | 1996
61
On Elastic-Plastic Stresses of a Sphere with Linear Hardening in a Discontinuous Temperature Field
Güven, U. | 1993
61
From Reissner Plate Theory to Three Dimensions in Large Deformation Shell Analysis
Ramm, E. | 2000
61
Applications of Parametric-Homogeneous Functions to Problems of Interaction between Fractal Surfaces
Borodich, F.M. | 1996
63
A numerical study on the suppression of draw resonance by inertia
Hagen, T. / Langwallner, B. | 2006
63
On the Underspread-Overspread Classification of Random Processes
Kozek, W. | 1996
63
Estimation and Modelling of Non stationary Stochastic Processes
| 1996
63
MINISYMPOSIUM 2: RANDELEMENTE IN DER DYNAMIK
| 1993
63
Minisymposium 5 - Robust Design - Designs of experiments in a polynomial regression when there is uncertainty about the degree
Dette, H. | 1999
63
2D, 21-2D, 3D Stress Finite Element Analysis of High Speed Heterogeneous Anisotropic Rotors of Gyroscopes and Ultracentrifuges
Borovkov, A.I. / Nikulina, L.V. / Shiryaev, P.M. | 1996
63
Analytic Solutions of Linear Second-Order Ordinary Differential Equations Governing the Wave Propagation in Non-Homogeneous Elastic Material
Wesolowski, Z. | 1993
64
On entropy conditions and traffic flow models
Knowles, J.K. | 2008
64
Book Review: Julius Wess, Theoretische Mechanik
Altenbach, H. | 2010
65
Jump and Transition Phenomena in Second Order Nonlinear Systems
Marée, G.J.M. | 1996
65
SHORT COMMUNICATIONS - Cohesive Damage Zone Model for a Circular Crack in a Quasi-Brittle Solid
Feng, X.-Q. | 2001
65
Calculations for central stress minimum under sand piles using continuum analysis
Altenbach, H. | 2010
65
Unstructured Mesh Generation and Adaption
Formaggia, L. | 1996
65
Modelling and simulation of fluid flows in a paper machine headbox
Hämäläinen, J. / Tiihonen, T. | 1996
65
The flow of a viscoelastic fluid on an oscillating plate
Hayat, T. / Mohyuddin, M.R. / Asghar, S. / Siddiqui, A.M. | 2004
65
SHORT COMMUNICATION - On the Motion of the Pendulum on an Ellipse
El-Barki, F.A. / Ismail, A.I. / Shaker, M.O. / Amer, T.S. | 1999
65
Numerical Procedures of Finite Element Elasto-Plastic Analysis of High Temperature Processes
Borovkov, A.I. / Semenov, A.S. | 1996
65
Book Review: B. Lapeyre, É. Pardoux and R. Sentis, Introduction to Monte-Carlo Methods for Transport and Diffusion Equations
Kloeden, P. | 2005
65
Fourierapproximation ohne Berechnung der Fourierkoeffizienten. Teil 1
Klingen, B. | 1994
65
On the Mechanism of Short Pitch Corrugation
Müller, S. | 2002
65
Modeling of Delamination Progress in Multilayered Composites by Energy Release Rates
Stein, E. / Tessmer, J. | 1998
66
On the Computation of Lamé Functions, of Eigenvalues and Eigenfunctions of Some Potential Operators
Ritter, S. | 1998
66
Two semi‐permeable equal collinear cracks weakening a piezoelectric plate – A study using complex variable technique
Bhargava, R. R / Jangid, Kamlesh / Verma, Pooja Raj | 2015
66
Acoustic radiation from a cylindrical source close to a rigid corner
Hasheminejad, S.M. / Azarpeyvand, M. | 2005
67
Fluid-Structural Coupling of Vibrating Bodies in a Surrounding Confined Liquid MA
Seemann, W. / Wauer, J. | 1996
67
Minisymposium 5 - Robust Design - The multi-point approximation method in a parallel computing environment
Keulen, F.von / Toropov, V.V. | 1999
67
Cover Picture: ZAMM 2-2009
| 2009
67
Signal Processing and Piecewise Convex Estimation
Riedel, K.S. | 1996
67
On the Nonlinear Theory of Nonsimple Thermoelastic Materials with Voids
Ciarletta, M. / Scalia, A. | 1993
67
Fluid-Structural Coupling of Vibrating Bodies in a Surrounding Confined Liquid
Seemann, W. / Wauer, J. | 1996
67
Geometrically Nonlinear Modelling of Elastic Mechanisms Using Helical Elements
Braun, M. / Stelzle, W. | 1996
67
An improved displacement boundary condition of piezoelectric cantilever beams
Lian-Zhi Yang / Liangliang Zhang / Lianying Yu / Minzhong Wang / Yang Gao | 2016
68
Boundary layers of the incompressible fluids for a permeable wall
| 2011
69
Coupled flow between saturated deformable porous medium and open domain in paper forming
Hiltunen, K. | 1996
69
A Subspace Study on Conjugate Gradient Algorithms
Yuan, Y.-X. / Stoer, J. | 1995
69
Contents: ZAMM 2-2009
| 2009
69
Zeitsynchrone sprungfreie Bahngeneratoren
Hoffmann, G. | 1994
69
The effect of thermal expansion on nonlinear first and second sound in superfluid Helium
Braun, S. / Kluwick, A. / Cramer, M.S. | 1996
69
Design of two-dimensional plane rapid expansion nozzles
Heynatz, J.T. | 2003
69
SHORT COMMUNICATIONS - An Isoperimetric Inequality for Eigenvalues of the Stekloff Problem
Brock, F. | 2001
69
Soil-Structure Interaction - Generalization of Reissner's Solution for the Viscoelastic Halfspace
Gaul, L. | 2000
69
Book Review: Canuto, C.; Hussaini, M.Y.; Quarteroni, A.; Zang, T.A., Spectral Methods. Fundamentals in Single Domains, Series: Scientific Computation, Volume package: Spectral Methods
Roos, H.-G. | 2007
69
Spline surfaces from irregular control meshes
Peters, J. | 1996
69
Jumping Behavior of the Reaction Rate of Fast Bimolecular Reactions
Nefedov, N.N. / Schneider, K.R. / Schuppert, A. | 1996
69
Wsgner W.; Gruttmann F.: Modeling of Fiber Reinforced Pobmer Structure? with Damage
| 1998
70
Book Review: A. Solodov and V. Ochkov, Differential Models - An Introduction with Mathcad
Platzer, B. | 2006
70
Fundamental Frequency of a Circular Plate Weakened along a Concentric Circle
Wang, C.Y. | 2002
70
Smoothness of weak solutions of the Ramberg-Osgood equations on plane domains
Bildhauer, M. / Fuchs, M. | 2007
71
Die Lagrangesche Transitivitätsgleichung
Bremer, H. | 1996
71
New Books - ZAMM 1-2004
| 2004
71
On the singularities of constrained tensegrity systems - application to a modified T3 model
Pirentis, A.P. / Markatis, S. / Lazopoulos, K.A. / Lazopoulos, A.K. | 2009
71
Minisymposium 5 - Robust Design - Design-of-experiments methods and their application to robust multicriteria optimization problems
Lautenschlager, U. / Eschenauer, H.A. / Mistree, F. | 1999
71
Book Review: Allaberen Ashyralyev and Pavel E. Sobolevskii, New Difference Schemes for Partial Differential Equations
Sonar, T. | 2006
71
Adaptively Wavelet-smoothed Wigner Estimated of Evolutionary Spectra
Sachs, R.von | 1996
71
A Nonnegative Criterion for Biconvex Functions
Jeyakumar, V. / Oettli, W. | 1994
72
The MHD boundary layer flow due to a rough rotating disk
Altenbach, J. | 2010
72
A hyperbolic model for granular flow
Cattani, A. / Colombo, R.M. / Guerra, G. | 2012
72
Stability of two superposed viscoelastic fluid-particle mixtures
Kumar, P. / Mohan, H. / Singh, G.J. | 2006
73
Variational Formulation and Existence of a Hydrodynamical Free Interface
Aguilar, J.-C. / Zolésio, J.P. | 1996
73
Identification of Drying Parameters for Paper Drying Model
Lepomäki, H. / Karlsson, M. / Nyström, L. / Luoma, M. | 1996
73
On Constructing Topologically Unrestricted B-Splines
Reif, U. | 1996
73
Weihe S.; Rinderlmecht S.; Kruger R.; Kroplin B.: Simulation of Fracture and Delamination Propagation in Fibre Reinforced Materials
| 1998
73
A novel method for the solution of the forward displacement problem of spherical parallel manipulators
Rodriguez, J. / Ruggiu, M. | 2013
73
Topological fluid mechanics with applications to free surfaces and axisymetric flows
Brøns, M. | 1996
74
Book Review: Hilary Ockendon and John R. Ockendon, Waves and Compressible Flow, in: J. E. Marsden, L. Sirovich, and S. S. Antman (eds.), Texts in Applied Mathematics, Vol. 47
Groves, M. | 2005
74
On the dynamic deformation of porous Cosserat linear-thermoelastic shells
Bîrsan, M. | 2008
75
Minisymposium 5 - Robust Design - New method of identification of mechanical properties of composite materials
Rikards, R. | 1999
75
Book Review: Stephen Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, in: J. E. Marsden, L. Sirovich, and S. S. Antman (Eds.), Texts in Applied Mathematics, Vol. 2.
Kloeden, P.E. | 2005
75
Multiblock Multigrid Grid Generation
Spitaleri, R.M. / Micacchi, V. | 1996
75
The Surface Temperature of a Halfplane Heated by Friction and Cooled by Convection
Fischer, F.D. / Werner, E. / Knothe, K. | 2001
75
Geometry and thermomechanics of structural rearrangements: Ekkehart Kröner's legacy Plenary lecture presented at the 80th Annual GAMM Conference, Augsburg, 25-28 March 2002
Maugin, G.A. | 2003
75
On the Asymptotic Analysis of Discontinuous Systems
Fidlin, A. | 2002
75
Ausbreitung von starken Druckwellen in der Atmosphäre
Gretler, W. | 1994
75
Cavity detection by the electric method: The 3-dimensional case
Ang, D.D. / Mennicken, R. / Thanh, D.N. / Trong, D.D. | 2004
75
Residual Stresses in an Elastic-Plastic Solid Shaft with Fixed Ends after Previous Rotation
Lindner, T. / Mack, W. | 1998
75
on the sections: Vibration and Stability Problems; Mechanics of Elastic and Plastic Bodies
| 1993
75
The Discrete Steady Sliding Problem
Klarbring, A. / Pang, J.-S. | 1999
75
Analysis of non-stationary and nonlinear signals
Subba Rao, T. | 1996
75
Spectral Properties of a System Describing Fast Pulsating DFB Lasers
Rehberg, J. / Wünsche, H.-J. / Bandelow, U. / Wenzel, H. | 1997
75
Dynamics of a simple rotating structure
Brøns, M. / Hjorth, P. / Kliem, W. | 1996
75
Book Review: Janusz Dyszlewicz, Micropolar Theory of Elasticity, in F. Pfeiffer and P. Wriggers (eds.), Lecture Notes in Applied and Computational Mechanics, Vol. 15
Altenbach, Holm | 2005
76
Book Review: Vitor Dias da Silva, Mechanics and Strength of Materials
Altenbach, J. | 2007
76
Supplement to the paper "Bounds for the extreme eigenvalues of symmetric matrices"
Piché, R. | 2005
77
Book Review: V. P. Maslov and G. A. Omel'yanov, Geometric Asymptotics for Nonlinear PDE I
Sonar, T. | 2006
77
Differential hierarchical models for elastic prismatic shells with microtemperatures
George Jaiani | 2015
77
Existence and Stability of the Optimum in Shape Optimization
Bucur, D. / Zolésio, J.-P. | 1996
77
Creeping Flow Past a Porous Spherical Shell
Yu, Qin / Kaloni, P.N. | 1993
77
A Universal Algorithm for Solving the Direct, Inverse, and Mixed Problems of the Airfoil Theory
Il'inskiy, N.B. / Fokin, D.A. | 1997
77
Plasticity and Damage of a Fiber Reinforced Aluminum Alloy: Expenments and Micromechanical Modeling
Werner, E. / Bohm, H.J. / Prantl, W. / Rarnmerstorfer, F.G. | 1998
77
Modelling of Coupled Heat and Mass Transfer in Copying Paper
Pietikäinen, R. / Tiihonen, T. | 1996
77
Experimental investigation of oscillating liquid droplets
Bruhn, D. / Hiller, W.J. / Kowalewski, T.A. / Obermeier, F. | 1996
78
On upper bounds for real proportional stabilizing controllers
Batra, P. | 2006
78
Existence and uniqueness for frictional incremental and rate problems - sharp critical bounds
L-E Andersson / A Pinto da Costa / M A Agwa | 2016
78
Frequency Response Plots: New Approaches
Parlett, B.N. / He, J. | 1996
78
The Eigenvalue and Inverse Eigenvalue Problems for Second Order Systems
| 1996
78
Book Review: Canuto, C. G., Hussaini, M. Y., Quarteroni, A., Zang, T. A., Spectral Methods. Evolution to Complex Geometries and Application to Fluid Dynamics, Series: Scientific Computation
Roos, H.-G. | 2008
79
Model Equations for Gravitational Sedimentation-Consolidation Processes
Bürger, R. / Wendland, W.L. / Concha, F. | 2000
79
A Posteriori Error Estimate of Approximate Solutions to a Special Nonlinear Elliptic Boundary Value Problem
Weisz, J. | 1995
79
In memory of Pavel Andreevich Zhilin (1942-2005)
Altenbach, H. / Indeitsev, D. / Ivanova, E. / Krvitsov, A. | 2007
79
Minisymposium 6 - Regelung mechanischer Systeme - Nonlinear control of planar parallel robots with redundant servopneumatic actuators
Hahn, H. / Klier, W. / Leimbach, K.-D. | 1999
79
A Mathematical Model for Deformation-Driven Experiments on Shape Memory Alloys
Bubner, N. | 1996
79
Sequential Regularization Methods for Nonlinear Higher Index DAEs
Ascher, U. / Lin, P. | 1996
79
A boundary integral equation formulation for the Helmholtz equation in a locally perturbed half-plane
Chandler-Wilde, S.N. / Peplow, A.T. | 2005
80
Prozesssimulation
Schuler, H. / Deuflhard | 1996
80
Strömungsmechanik
Oertel Jr, H. / Strobel | 1996
81
Homogenization of Two Phase Flow through Randomly Heterogeneous Porous Media
Badea, A. / Bourgeat, A. | 1996
81
Hedging in Illiquid Markets: Nonlinear Effects
Schönbucher, P. / Wilmott, P. | 1996
81
Mathematical Finance
| 1996
81
Riemann Boundary Value Problem Technique for Solving Multiple Simultaneous Series Relations Involving Trigonometric Functions
Srivastava, N. / Srivastava, K.N. | 1995
81
Improvement of Mechanical Composite Properties by Interlayer Tayloring on Atomic Scale
Woltersdorf, J. / Pippel, E. / Hähnel, A. | 1998
81
Contents: ZAMM 2-2008
| 2008
81
Influence of rotary inertia on the fiber dynamics in homogeneous creeping flows
Altenbach, H. / Naumenko, K. / Pylypenko, S. / Renner, B. | 2007
81
Nonsimilar MHD Boundary Layer Flow Near an Asymmetric Plane Stagnation Point MA
Salcudean, M. / Nowak, Z.P. / Sam, Lawrence P. / Nageswara, Rao B. | 1996
81
Finite-Elemente-Formulierung des 3D-Kolltaktproblems unter Berücksichtigung eines verfestigenden Reibungsgesetzes
Buczkowski, R. / Gabbert, U. | 1996
81
New Intrinsic Models for Shells
Delfour, M. / Zolésio, J.-P. | 1996
83
Contents: ZAMM 2–3
| 2013
83
Allgemeine nichtlineare Stabilitätsgleichungen für gerade Stäbe und ihre Anwendung auf kinetische Kippprobleme
Büllesbach, J. / Heinen, A.H. | 1996
83
Constraint Preserving Integrators for Unstructured Higher Index DAEs
Campbell, S. / Moore, E. / Zhong, Y. | 1996
83
Book Review: Dieter Schroeder, Vektor- und Tensorpraxis
| 2010
83
Minisymposium 6 - Regelung mechanischer Systeme - Lineare Positionsregelung nichtlinearer mechanischer Systeme
Müller, P.C. | 1999
83
Editorial: ZAMM 2-2008
Altenbach, H. | 2008
83
Book Reviews: Rolf Mahnken, Lehrbuch der Technischen Mechanik - Dynamik. Eine anschauliche Einführung
Eremeyev, V.A. | 2010
83
Book Review: Ever J. Barbero, Finite Element Analysis of Composite Materials
Ito, Susumu / Raviola, Elio | 2010
83
Optimal Control of a Phase-Field Model Using Proper Orthogonal Decomposition
Volkwein, S. | 2001
83
A General View of Minimally Extended Systems for Simple Bifurcation Points
Allgower, E.L. / Schwetlick, H. | 1997
84
Congratulation: Franz Ziegler
Adam, C. / Heuer, R. / Irschik, H. / Rammerstorfer, F.G. | 2008
84
Book Review: Tuncer Cebeci, Turbulence Models and Their Application. Efficient Numerical Methods with Computer Programs
Niggemann, M. | 2006
84
Book Review: Leonid P. Lebedev and Michael J. Cloud, Introduction to Mathematical Elasticity
Ainsworth, SophieJ. / Stanley, RachaelL. / Evans, DarrellJ.R. | 2010
84
Approximation of the Complementary Error Function
Heinz, C. | 1995
85
Contents: ZAMM 2/2010
Moreno-Egea, Alfredo / Bustos, José Antonio Castillo / Girela, Enrique / Aguayo-Albasini, José Luis | 2010
85
Der Aufprall eines Balles auf eine starre Wand
Greimel, R. | 1995
85
Shape Boundary Derivative of Tangential Boundary Value Problems
Desaint, F. / Zolésio, J.-P. | 1996
85
Option Pricing, Transaction Costs and Nonlinearities
Wilmott, P. / Whalley, A.E. | 1996
85
Discretized Landweber Iteration Methods for Nonlinear Inverse Problems
Ramlau, R. | 1998
85
An Extended Liapunov Approach to the Stability Assessment of Marine Risers
Köhl, M. | 1993
85
Measuring of Molecular Effect in Overstrained Polymeres Using Infrared Absorptionspectroscopy
Buhler, J. | 1996
85
Effective properties of irregularly reinforced materials
Bakhvalov, N.S. | 1996
85
Book Review: Gerhard Knappstein, Aufgaben zur Festigkeitslehre – ausführlich gelöst. Mit Grundbegriffen, Formeln, Fragen, Antworten
| 2011
85
Contents: ZAMM 3/2010
Lazopoulos, K.A. / Lazopoulos, A.K. | 2010
85
Book Review: Claus‐Dieter Munz und Thomas Westermann, Numerische Behandlung gewöhnlicher und partieller Differenzialgleichungen
| 2011
85
Vortex stretching driven by Jeffery-Hamel flow
Zaturska, M.B. / Banks, W.H.H. | 2003
86
Effects of material inhomogeneity on the dynamic behavior of cracked piezoelectric solids: a BIEM approach
Rangelov, T. / Dineva, P. / Gross, D. | 2008
86
Wavelets
Louis, A.K. / Maass, P. / Rieder, A. / Roos | 1996
86
Dynamische Systeme (Reference)
Arrowsmith, D.K. / Place, C.M. | 1996
86
Book Review: Thomas Westermann, Modellbildung und Simulation – Mit einer Einführung in ANSYS
| 2011
86
2D shape optimization of turbine blades
Montrone, F. / Wever, U. / Zheng, Q. | 2004
86
Sternstunden der Physik
Newton, R.G. / Schöpf | 1996
87
Der hydraulische Mechanismus des Spinnenbeines und seine Anwendung für technische Probleme
Bohmann, L. / Blickhan, R. | 1998
87
Tensorgeneratoren bei Systemen von Tensoren zweiter und vierter Stufe MA
Betten, J. / Helisch, W. | 1996
87
Modellierung und Analyse der Stossvorgänge bei einer zweibeinigen Gehmaschine
Buschmann, A. / Frik, M. | 1996
87
Editorial: ZAMM 2–3
Diebels, Stefan | 2013
87
Tensorgeneratoren bei Systemen von Tensoren zweiter und vierter Stufe
Betten, J. / Helisch, W. | 1996
87
A General Solution Technique for Piezothermoelasticity of Hexagonal Solids ot Class 6 mm in Cartesian Coordinates
Ashida, F. / Tauchert, Th R. / Noda, N. | 1994
87
Contents: ZAMM 2
| 2011
87
Dichotomic Stability and Multiple Shooting for Numerical Boundary-Value Problems in Index-One Differential-Algebraic Equations
England, R. / Lamour, R. | 1996
87
Multibody system dynamics and mechatronics
Hiller, M.H. / Hirsch, K. | 2006
87
Minisymposium 6 - Regelung mechanischer Systeme - Robust control of an aircraft model
Werner, H. | 1999
88
Modeling FGM brake disk against global thermoelastic instability (hot-spot)
Hernik, S. | 2009
88
Damage of nonlinearly elastic materials at small strain - Existence and regularity results -
Kruglikova, Irina / Grantcharov, Teodor P. / Drewes, Asbjorn M. / Funch-Jensen, Peter | 2010
88
Book Review: D. Chapelle and K.-J. Bathe, The Finite Element Analysis of Shells - Fundamentals.
Marti, K. | 2005
88
Parameter re‐identification in nanoindentation problems of viscoelastic polymer layers: small deformation
Chen, Z. / Diebels, S. | 2013
89
The basin of attraction of periodic orbits in nonsmooth differential equations
Giesl, P. | 2005
89
Mathematical Modelling of the Stress Distribution in High Field Magnet Coils
Caldwell, J. | 1996
89
Shape Sensitivity Analysis: An Application to a Free Boundary Problem
Dziri, R. / Zolésio, J.-P. | 1996
89
Low-Frequency Dispersion-Function Factorization and Classification of P-SV Modes by Wavenumber Limits
lvansson, S. | 2002
89
Control Problems for Distributed Parameter Systems with Applications
| 1996
89
Pontryagin's Principle for State-Constrained Control Problems governed by Parabolic Equations
Casas, E. | 1996
89
Averaged equations for statics and dynamics of incompressible elastic media with pores
Eglit, M.E. | 1996
89
Darboux Transformations and Global Information in Inverse Theory
Sabatier, P.C. | 1998
90
Generalized continua and non‐homogeneous boundary conditions in homogenisation methods
| 2011
91
Vertical stress distribution in isotropic half‐spaces due to surface vertical loadings acting over polygonal domains
D'Urso, Maria Grazia / Marmo, Francesco | 2015
91
Mode Analysis of Taylor-Couette Flow in Finite Gaps
Berger, H.-R. | 1999
91
Residual based sampling in POD model order reduction of drift‐diffusion equations in parametrized electrical networks
Hinze, M. / Kunkel, M. | 2012
91
On the Numerical Solution of Semilinear Parabolic Problems in Multicomponent Structures with Volterra Operators in the Transmission Conditions and in the Boundary Conditions
Kacur, J. / Kerr, R.van | 1995
91
The differential-algebraic index concept in electric circuit simulation
Günther, M. / Rentrop, P. | 1996
91
Minisymposium 7 - Nichtglatte Systeme - Discussion of d 'Alemberts principle for non-smooth unilateral constraints
Glocker, Ch | 1999
91
Turbulenzstruktur und statistische Eigenschaften der Trennschicht in inneren turbulenten Drallströmungen
Cantrak, S. / Benisek, M. / Nedelkovic, M. | 1996
93
Monte-Carlo Simulations for Stochastic Homogenization
Hornung, U. / Kelanemer, Y. | 1996
93
Formulation of Fluid-Structure-Interaction by Hybrid Boundary Integral Method
Gaul, L. / Wagner, M. | 1998
93
Modelling nonlinear dynamics of shape-memory-alloys with approximate models of coupled thermoelasticity
Melnik, R.V.N. / Roberts, A.J. | 2003
93
The Existence and Uniqueness of Solutions by the Covering Domain Method in Linear Elastostatics
Lin, X. / Ballmann, J. | 1996
93
The Existence and Uniqueness of Solutions by the Covering Domain Method in Linear Elastostatics MA
Lin, X. / Ballmann, J. | 1996
93
Subharmonic Vibrations and Chaos in Forced Nonlinear Oscillators
Schmidt, G. / Seisl, M. | 1993
93
Modelling and Analysis of Dynamic Contact Problems in Travelling Wave Ultrasonic Motors
Cao, X. / Wallaschek, J. | 1996
93
Some aspects of the approximate controllability properties of the semi linear distributed parameter systems
Khapalov, A.Y. | 1996
93
Shape Hessian for a Non Differentiable Variational Free Boundary Problem
Guido, Y. / Zolésio, J.-P. | 1996
94
On constitutive inequalities in nonlinear theory of elastic shells
Eremeyev, V. / Zubov, L. | 2007
95
Minisymposium 7 - Nichtglatte Systeme - Experiments, modelling and analysis of friction and impact oscillators
Hinrichs, N. / Oestreich, M. / Popp, K. | 1999
95
Boundary Integrals Method for the Magnetohydrodynamic Duct Flow
Carabineanu, A. / Oprea, I. | 1996
95
On a Generalization of a Theorem of von Neumann
Hairer, E. / Wanner, G. | 1996
96
Micropolar fluid flow due to rotating and oscillating circular cylinder: 6th order numerical study
Kamal, M.A. / Siddiqui, A.Z.A. | 2004
97
Modelling Stress Evolution During Cable Fabrication
Bailey, C. / Clapham, S. / Cross, M. / Dixon, T. / Wolfe, S. / Norman, P. | 1996
97
Fluids with Transverse Isotropy as Models for Electrorheological Fluids
Brunn, P.O. / Abu-Jdayil, B. | 1998
97
Attitude Drift of a Dissipative, Torquefree, Radially Deformable Gyro
Rimrott, F.P.J. / Semenov, G. | 1994
97
Transient Motion of a Viscous Liquid with Free Surface in a Cylindrical Container
Bauer, H.F. / Eidel, W. | 1999
97
An Algorithmic Approach to DOE - Algebraic Methods
Fontana, R. | 1996
97
Minisymposium 7 - Nichtglatte Systeme - Periodic solutions of conservative non-smooth dynamical systems
Kunze, M. | 1999
97
Design of Real and Simulated Experiments in Industrial Product Optimization
| 1996
97
Interaction of Standing Waves
Schatzmann, M. | 1996
97
Rollen einer starren Walze auf einem elastischen Streifen
Brommundt, E. | 1998
97
Deterministic Particle Simulation of Multiheterojunction Bipolar Semiconductor Devices: The Semiclassical Case
Barrio, E.Cebrián de / Moreno, Fco J.Mustieles | 1996
98
Existence and Stability of Normal Motions in Loaded Hydraulic Copying Systems with Periodic and Composed Inputs
Halanay Jr, A. / Safta, C.A. | 2000
99
Uniqueness and Non-uniqueness in the Steady Displacement of Two Visco-plastic Fluids
Frigaard, I.A. / Scherzer, O. / Sona, G. | 2001
99
Transporting and Mixing Gasses with Different Qualities
Kate, H.ten / Hoeven, T.van der / Sierksma, G. | 1997
99
On Asymptotics in Case of Dae's
Hanke, M. / März, R. | 1996
99
A Computational Model of Pulsed-Laser Irradiation of Hydrogenated Amorphous Silicon with Phase Changes
Cerny, R. / Prikryl, P. | 1996
100
Eigenfunctions of the 2-dimensional anisotropic elasticity operator and algebraic equivalent materials
Specovius-Neugebauer, M. / Steigemann, M. | 2008
101
The Numerical Modelling of Multi-Physics Phenomena: The Shape Casting Process
Chow, P. / Bailey, C. / Cross, M. / Pericleous, K.A. | 1996
101
Optimization of Physical and Mechanical Properties of Laminated Filters and Combinations
Chigarev, A.V. / Rafeenko, E.D. | 1996
101
Minisymposium 7 - Nichtglatte Systeme - Applications of non-smooth mechanical systems: An overview
Popp, K. | 1999
101
Nichtlineare Radsatz-Gleis Wechselwirkung und Riffelwachtstum
Ilias, H. / Knothe, K. | 1998
101
Concentration Sets for 2-D Incompressible Flow
Lopes-Filho, M.C. / Nussenzveig Lopes, H.J. | 1996
101
An Approximate Newton-Like Coupling of Subsystems
Menck, J. | 2002
101
An Algorithmic Approach to DOE - Geometrical Methods
Pistone, G. | 1996
102
Modelling the hydrothermomechanical properties of polymers close to glass transition
Engelhard, M. / Lion, A. | 2013
102
On new phase inclusions in elastic solids
Freidin, A.B. | 2007
103
Using Proportional and Derivative Output Feedback in Regularizing Singular Systems
Chu, D.L. / Chan, H.C. / Ho, D.W.C. | 1996
103
A stable realization of lower index DAE transfer methods
Petry, T. | 1996
103
On the Stefan Problem with Different Phase Densities
Starovoitov, V.N. | 2000
104
Book Review: Ronald A. DeVore, Arieh Iserles, and Endre Süli (eds.), Foundations of Computational Mathematics.
Kloeden, P.E. | 2005
105
Splitting of energy of dispersive waves in a star-shaped network
Mehmeti, F.Ali / Régnier, V. | 2003
105
On the Complexity of Multivariate Integral Equations in Sobolev Space
Frank, K. | 1996
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