  While the use of technology to provide accurate and objective measurements of
human movement performance is presently an area of great interest, efforts to
quantify the performance of movement are hampered by the lack of a principled
model that describes how a subject goes about making a movement. We put forward
a principled mathematical formalism that describes human movements using an
optimal control model in which the subject controls the jerk of the movement.
We construct the formalism by assuming that the movement a subject chooses to
make is better than the alternatives. We quantify the relative quality of
movements mathematically by specifying a cost functional that assigns a
numerical value to every possible movement; the subject makes the movement that
minimizes the cost functional. We develop the mathematical structure of
movements that minimize a cost functional, and observe that this development
parallels the development of analytical mechanics from the Principle of Least
Action. We derive a constant of the motion for human movements that plays a
role that is analogous to the role that the energy plays in classical
mechanics. We apply the formalism to the description of two movements: (1)
rapid, targeted movements of a computer mouse, and (2) finger-tapping, and show
that the constant of the motion that we have derived provides a useful value
with which we can characterize the performance of the movements. In the case of
rapid, targeted movements of a computer mouse, we show how the model of human
movement that we have developed can be made to agree with Fitts' law, and we
show how Fitts' law is related to the constant of the motion that we have
derived. We finally show that solutions exist within the model of human
movements that exhibit an oscillatory character reminiscent of tremor.
