Consider a satellite in a circular orbit around the earth. Then properties of the satellite depend on the radius of the orbit r as follows: speed time period angular momentum and kinetic energy
For a satellite in a circular orbit
The phase space diagram for free particle motion
For the Lagrangian
find equation of motion
Correct Answer :- d
Explanation : L = (x2+ x,2y2)/2 - kx,2y2/2
d/dt(dL/dx) - dL/dx = 0
=> d/dt(x) - xy2 + kxy2 = 0
=> x = xy2 - kxy2
d/dt(dL/dy) - dL/dy = 0
d/dt(x2y) + kx2y = 0
=> x2y + 2xy + kx2y = 0
xy = -2xy - kxy
The value of is
From the Poisson's bracket
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