This preview shows page 1. Sign up to view the full content.
Unformatted text preview: Homework 5 Classical Mechanics (Phys701) Due: October 10, 2011 Problem 17 Show that Lagrange’s equations can also be written as ∂ ˙ T ∂ ˙ q j 2 ∂T ∂q j = Q j . These are sometimes known as the Nielsen form of the Lagrange equations. (Hint: start with writing a formula for ˙ T ). Problem 19 The electromagnetic field is invariant under a gauge transformation of the scalar and vector potentials given by A → A + ∇ Ψ( r, t ) , ϕ → ϕ 1 c ∂ Ψ ∂t , where Ψ is an arbitrary (but differentiable). What effect does this gauge transformation have on the Lagrangian of a particle moving in the electromagnetic field? Is the motion affected? Problem 121 Two mass points of mass m 1 and m 2 are connected by a string passing through a hole in a smooth table so that m 1 rests on the table surface and m 2 hangs suspended. Assuming m 2 moves only only in a vertical line, what are the generalized coordinates for the system? Write the Lagrange equations for the system and, if possible, discuss the physical significance any of them might...
View
Full
Document
This note was uploaded on 12/13/2011 for the course PHYS 701 taught by Professor Bazaliy during the Fall '11 term at South Carolina.
 Fall '11
 Bazaliy
 mechanics, Work

Click to edit the document details