Starting from rest at time (t=0) and at altitude (h_{0}), a block of mass (M) slides down
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Starting from rest at time \(t=0\) and at altitude \(h_{0}\), a block of mass \(M\) slides down a frictionless plane inclined at angle \(\alpha\) to the horizontal. There is a uniform gravitational field \(g\) directed vertically downward.
(a) Write the Hamilton-Jacobi equation for the block.
(b) Solve the equation to find Hamilton's principal function \(S\).
(c) Find the equation of motion \(s(t)\) for the block, where \(s\) is the distance along the incline, measured from the top of the incline.
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