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Mathematical Methods of Classical Mechanics
Vladimir I. Arnold
- 01 Jan 1974
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TL;DR: In this paper, Newtonian mechanics: experimental facts investigation of the equations of motion, variational principles Lagrangian mechanics on manifolds oscillations rigid bodies, differential forms symplectic manifolds canonical formalism introduction to pertubation theory.
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Abstract: Part 1 Newtonian mechanics: experimental facts investigation of the equations of motion. Part 2 Lagrangian mechanics: variational principles Lagrangian mechanics on manifolds oscillations rigid bodies. Part 3 Hamiltonian mechanics: differential forms symplectic manifolds canonical formalism introduction to pertubation theory.
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Citations
Graphical evolution of the arnold web: from order to chaos
TL;DR: This work represents graphically the evolution of the set of resonances of a quasi-integrable dynamical system, the so-called Arnold web, whose structure is crucial for the stability properties of the system.
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Contact Hamiltonian Mechanics
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Energy-minimizing splines in manifolds
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TL;DR: The definition of the familiar cubic spline curves and splines in tension is extended, and it is shown how to compute these on parametric surfaces, level sets, triangle meshes, and point samples of surfaces.
Symmetries and conserved quantities of constrained mechanical systems
TL;DR: In this article, the Lie symmetries and conserved quantities of constrained mechanical systems are studied using the invariance of the ordinary differential equations under the infinitesimal transformations.
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