Mathematical Methods of Classical Mechanics
@inproceedings{Arnold1974MathematicalMO,
title={Mathematical Methods of Classical Mechanics},
author={Vladimir I. Arnold},
year={1974}
}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.
11,606 Citations
HAMILTONIAN MECHANICS ON KÄHLER MANIFOLDS
- Mathematics
- 2006
Using the mechanical principle, the theory of modern geometry and advanced calculus, Hamiltonian mechanics was generalized to Kahler manifolds, and the Hamiltonian mechanics on Kahler manifolds was…
Variational principle in Hamiltonian mechanics
- Physics
- 2008
In this paper, special features of the variational principle in Hamiltonian mechanics (the problem of covariant formulation and boundary conditions) are analyzed; the difference between the…
Newtonian Mechanics on Kähler Manifold
- Mathematics, Physics
- 1996
In this paper we discuss Newtonian Mechanics on Kähler Manifold, and also give the complex mathematical aspects of Newton's law, the law of kinetic energy, the law of kinetic quantity, the equation…
LAGRANGIAN MECHANICS ON KAHLER MANIFOLDS
- Mathematics
- 2005
Lagrangian mechanics on Kahler manifolds were discussed, and the complex mathematical aspects of Lagrangian operator, Lagrange's equation, the action functional, Hamilton's principle, Hamilton's…
On the Geometry of Variational Principles of Physics
- Physics, Mathematics
- 2003
The essentials of the invariant mathematical apparatus used for geometrization of basic variational principles of physics and mechanics are presented. An important connection between the geometry of…
Formulations of Classical Mechanics
- PhysicsThe Routledge Companion to Philosophy of Physics
- 2021
I outline three formulations of classical mechanics, Newtonian, Lagrangian, and Hamiltonian mechanics, that are ordinarily seen as fully equivalent—notational variants of a single theory. I point to…
Contact Hamiltonian mechanics. An extension of symplectic Hamiltonian mechanics
- PhysicsJournal of Physics: Conference Series
- 2018
This contribution gives a possible solution of the major question whether it is possible to construct a classical mechanical theory which not only contains all the advantages of the Hamiltonian…
Classical Mechanics and Poisson Structures
- Mathematics
- 2015
In this chapter, we will briefly recall the Hamiltonian formulation of classical mechanics, focusing in particular on its algebraic aspects. In this framework, a classical system will be described by…
Gauge theory in Hamiltonian classical mechanics : The electromagnetic and gravitational fields
- Physics, Geology
- 1979
Gauge potentials are directly defined from Hamiltonian classical mechanics. Gauge transformations belong to canonical transformations and are determined by a first order development of generating…