Lagrangian mechanics

Mathematician and astronomer (1736–1813)

one of five positions in an orbital configuration of two large bodies where a small object can maintain a stable relative position

formulation of classical mechanics based on the Lagrangian function on the tangent bundle of configuration space

physical quantity of dimension energy × time

principle

parameters that describe the configuration of the system relative to some reference configuration

physical theory describing classical fields

principle that the dynamics of a physical system are determined by a variational problem of the Lagrangian

periodic, three-dimensional orbit near the L1, L2 or L3 Lagrange points in the three-body problem of orbital mechanics

quasi-periodic orbital trajectory

derivative of a function of several variables with respect to one variable, without the others held constant

property of a dynamical system where solutions near an equilibrium point remain so

Displacement in analytical mechanics

sets of coordinates which can be used to describe a physical system at any given point in time

in analytical mechanics, the rate of change of the virtual work along generalized coordinates

simplification of coordinates for an n-body system

function used in Lagrangian mechanics

canonical differential form defined on the cotangent bundle of a smooth manifold

type of system in classical mechanics

field theory coupling of charge but not higher moments

A mechanical system is scleronomous if the equations of constraints do not contain the time as an explicit variable and the equation of constraints can be described by generalized coordinates. Such constraints are called scleronomic constraints. The opposite of scleronomous is rheonomous.