State-Space Transformation 

Obtain the governing equations of a spherical pendulum in Cartesian coordinates, put them into the affine state-space form, and convert them to spherical coordinates.

The governing equations from the Lagrangian.

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The affine representation with states and inputs .

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The transformation between spherical and Cartesian coordinates.

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The transformation of the coordinate derivatives.

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The complete state transformation.

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The expressions in spherical coordinates are much simpler.

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