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Dynamics is a branch of applied mathematics (specifically classical mechanics) concerned with the study of forces and torques and their effect on motion, as opposed to kinematics, which studies the motion of objects without reference to its causes.

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Yes, a state matrix with zero rows and/or columns makes sense and is viable. It typically signify pure integrators in the system. In the example you give, $$ \dot{v} = -\frac{b}{m} v +\frac{1}{m} u …
answered Jun 7 '17 by Christo