Contents 1 Particle Kinematics 1 1.1Introduction..... 1 1.2SingleParticleKinematics..... 4 1.2.1Motionincon **gurationspace**..... 4

ThefunctionsÁ r depend on the q'salone (hence then am e`pointtransformation') , and they specify the transformation: we viewitasageometricalpoint-to-point mapping in con ¯**gurationspace**.

Assuming that the system can, at least on average, be fully described by the two parameters a and, we can plot the evolution of activity propagation as trajectories in the ( a , )-con"**gurationspace**.

Points in con-**gurationspace** correspond to congurationsof the pair. The conguration space partitions into blocked space where the parts overlap, free space where they are separate, and contact space where they touch.

planinthestatespacesimilarlytoplanninginthecon **gurationspace**.Inthis way the techniques described in previous sections can be adapted to deal this

... the human nervous system, however, so the approach of using observed data to estimate probability distributions overcontrol space is very appealing. 3.1 A Model for Control By collecting data from real human motion our system mo dels behavior patterns as statistical densities over con-**gurationspace**.

Brizard Saint Michael'sCollege Lagrangian Mech anics 1Principleof Least Action The con¯gurationofa mechanical system evolving in ann-dimensional space, with coordinates x=(x 1; x 2; :::;x n), maybe described in terms of generalized coordi natesq= (q 1;q 2;: ::;q k)inak-dimensional con¯**gurationspace** ...

L+ e c rÂ¢ _ x¡e Ã ¡ 1 c @Â @t! =L+ e c dÂ dt: As is generally known, since Lagrangians can only be de¯neduptotheexact time derivative ofatime-de pendent function on con¯**gurationspace** (i.e., equivalent Lag rangiansyield the same Euler-Lagrange equations), we ¯ndthatagauge transformation keeps the Lagrangian ...

Thed-adjacency con **guration space** isthesubgraphofthecon **gurationspace** in which moves are restricted to be d-adjacent. Studying connectivity in this

Brooks shows how parametric variable scan be propagated through an assembly and Donald treats parametric variables as additional dimension sin con®**gurationspace**.