Mathematical Methods of Classical Mechanics

  title={Mathematical Methods of Classical Mechanics},
  author={Vladimir I. Arnold},
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. 


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

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

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 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

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

  • Jill North
  • Physics
    The 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

  • H. Cruz
  • Physics
    Journal 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

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

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

Contact Hamiltonian Mechanics