Lagrange Equation Part 01/ Derivation of Lagrange Equation
Channel: Physics Master
Date: 2020-06-03

Classical Mechanics Lecture 02 Part 1.
Derivation of Lagrangian Equation for Non-Conservative Holonomic System. In this lecture we derived the Lagrange equation for a non, conservative Holonomic system using the d'alembert's principle. Lagrange equation is the core of this course that shall help you with the upcoming lectures and classes.
Elegant and powerful methods have also been devised for solving dynamic problems with constraints. One of the best known is called Lagrange’s equations. The Lagrangian L is defined as L = T − V, where T is the kinetic energy and V the potential energy of the system in question. Generally speaking, the potential energy of a system depends on the coordinates of all its particles; this may be written as V = V(x 1, y 1, z 1, x 2, y 2, z 2, . . . ). The kinetic energy generally depends on the velocities, which, using the notation v x = dx/dt = ẋ, may be written T = T(ẋ 1, ẏ 1, ż 1, ẋ 2, ẏ 2, ż 2, . . . ). Thus, a dynamic problem has six dynamic variables for each particle—that is, x, y, z and ẋ, ẏ, ż—and the Lagrangian depends on all 6N variables if there are N particles.