Antisymmetric and Orthogonal Matrices 

If is an antisymmetric matrix and is a vector obeying the differential equation , then has constant magnitude. Consider first a constant matrix.

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The solution to the differential equation can be written down using MatrixExp.

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Verify that is indeed a solution.

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The matrix used to define the solution is orthogonal.

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Solutions to constant coefficient equations trace repeating circles on the sphere.

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Solutions for a nonconstant coefficient matrix might require numerical solutions.

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While motion is still restricted to a sphere, more interesting patterns are now possible.

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