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23 Nov 2019

L= 1/2 m (x_1'^2 + x_2'^2) + α/r

show that if x_i* = x_i + ε/2 (2p_i x_s -x_i p_s - δ_is (r *p)) Where ε is small and s equal to 1 and "_" indicates subscript

that the change in the lagrangian

δL = ε*m*α d/dt (x_s/r)

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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

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A particle of mass m moves under the influence of a central force.The potential energy function is
V(r) = {
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as illustrated in the figure. The initial position is (x,y) = (a/2,0) and the initial velocity is (vx,vy) = (0, v0).
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***HINT GIVEN***

Use the constants of the motion to analyze the orbit.

Write L = mr^2 dφ/dt = the initial value.
What is the initial value?


Write E = (1/2)m (dr/dt)^2 + L^2/(2mr2) +V(r )
= the initial value. What is the
initial value?

Part A. In the energy equation,
change the variable from r to u,
where r =sqrt(u). The result can be
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