Problem

A particle of mass m moving in three dimensions under the potential energy function V(x, y...

A particle of mass m moving in three dimensions under the potential energy function V(x, y, z) = αx + βy2 + γz3 has speed v0 when it passes through the origin.

(a) What will its speed be if and when it passes through the point (1,1,1)?


(b)  If the point (1, 1, 1) is a turning point in the motion (v = 0), what is v0?


(c) What are the component differential equations of motion of the particle?

(Note: It is not necessary to solve the differential equations of motion in this problem.)

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