We can use the calculus of variations to solve a classic problem in the history ofphysics the branchistochrome.Consider a particle moving in a constant force field startingat rest from some point (x1,y1) to some lower point (x2,y2).Find a suitable set of generalized coordinates for point particle moving on the surface of a hemisphere of radius R whose center is at the origin.

NOTE: Quantity that needs to be determined is not given in the brachistochrone problem. Hence, the…

Answered: Find a suitable set of generalized…

Find a suitable set of generalized coordinates for point particle moving on the surface of a hemisphere of radius R whose center is at the origin.

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Question

We can use the calculus of variations to solve a classic problem in the history of
physics the branchistochrome.Consider a particle moving in a constant force field starting
at rest from some point (x₁,y₁) to some lower point (x₂,y₂).

Find a suitable set of generalized coordinates for point particle moving on the surface of
a hemisphere of radius R whose center is at the origin.

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