Lecture 1F, 08 Jan 1999
1. The state space and its tangent spaces
| This is an exemplary one-dimensional state space, S. The point, p, represents a virtual state of some system. |
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| This is a secant line. Think of the right end point as a sliding bead, and the left endpoint, p, as a rotating hinge. |
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| As the sliding bead moves to the rotating hinge, the secant line becomes tangent to the state space. This tangent line is the tangent space to S at the point p. |
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