problems_HW5 - Homework 5 Classical Mechanics (Phys701)...

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Unformatted text preview: Homework 5 Classical Mechanics (Phys701) Due: October 10, 2011 Problem 1-7 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 1-9 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 1-21 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...
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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.

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