In physics, Lagrangian mechanics is a formulation of classical mechanics founded on the stationary-action principle (also known as the principle of least action). It was introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange in his 1788 work, Mécanique analytique.Lagrangian mechanics describes a mechanical system as a pair (M,L) consisting of a configuration space M and a smooth function L within that space called a Lagrangian. For many systems, L = T - V, where T and V are the kinetic and potential energy of the system, respectively.The stationary action principle requires that the action functional of the system derived from L must remain at a stationary point (a maximum, minimum, or saddle) throughout the time evolution of the system. This constraint allows t
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Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery and astronomical objects, such as spacecraft, planets, stars, and galaxi
Hamiltonian mechanics emerged in 1833 as a reformulation of Lagrangian mechanics. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics replaces (generalized) velocities \dot q^i
In physics, angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved
Présentation des méthodes de la mécanique analytique (équations de Lagrange et de Hamilton) et introduction aux notions de modes normaux et de stabilité.
This course introduces students to continuous, nonlinear optimization. We study the theory of optimization with continuous variables (with full proofs), and we analyze and implement important algorithms to solve constrained and unconstrained problems.
The existence of at least two homoclinic orbits is proved by A. Ambrosetti and V. Coti Zelati (Multiple homoclinic orbits for a class of conservative systems, Rend. Sem. Mat. Univ. Padova, 89 (1993), 177-194) for autonomous Lagrangian systems
In this paper, we consider a compact connected manifold (X, g) of negative curvature, and a family of semi-classical Lagrangian states f(h)(x) = a(x)e(i phi(x)/h) on X. For a wide family of phases phi, we show that f(h), when evolved by the semi-classical Schrodinger equation during a long time, resembles a random Gaussian field. This can be seen as an analogue of Berry's random waves conjecture for Lagrangian states.