Let (a) Show that the solution to the linear system x = Ax represents a rotation of
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Let
(a) Show that the solution to the linear system ẋ = Ax represents a rotation of R3 around the z-axis. What is the trajectory of a point x0?
(b) Show that the solution to the inhomogeneous system ẋ = Ax + b represents a screw motion of R3 around the z-axis. What is the trajectory of a point x0?
(c) More generally, given 0 ≠ a ∈ R3, show that the solution to ẋ = a × x + a represents a family of screw motions along the axis a.
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ANSWER a The matrix A can be written as A 0 1 0 1 0 0 0 0 0 Let xt be a solution to x Ax Then we hav...View the full answer
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