Consider the following system of second-order initial-value problems: = u(t) u"(t) (0) = 1, 2 (0) = 0, (2) (u(t)2 + v(t)

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Consider The Following System Of Second Order Initial Value Problems U T U T 0 1 2 0 0 2 U T 2 V T 1 (44.99 KiB) Viewed 51 times

Consider the following system of second-order initial-value problems: = u(t) u"(t) (0) = 1, 2 (0) = 0, (2) (u(t)2 + v(t)2)3/2 v(t) v"(t) v(0) = 0, v'(0) = 1. (3) (u(t)2 + v(t)2)3/2' These are Newton's equations of motion for the two-body problem, also known as the Kepler problem. Here the pair (u(t), v(t)) describes the trajectory of one of the bodies at time t. If we let t range from 0 to 27, then the solution will be a circle. (a) (3pts) Transform the given problem into an appropriate system of first-order initial-value problems.