Asked by pete
study the motion of a particle of mass m in a central potential U(r) = γr^2 with
γ > 0.
a) write the equations of motion in cartesian coordinates (x, y, z). are they coupled or independent with each other?
b) solve the equation of motion for x, y, and z directions.
c) is the angular momentum conserved? can you select a special coordinate system to simplify the problem?
d) can the orbit be an ellipse? if yes, what conditions should the parameters in your solution satisfy?
γ > 0.
a) write the equations of motion in cartesian coordinates (x, y, z). are they coupled or independent with each other?
b) solve the equation of motion for x, y, and z directions.
c) is the angular momentum conserved? can you select a special coordinate system to simplify the problem?
d) can the orbit be an ellipse? if yes, what conditions should the parameters in your solution satisfy?
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