Dirac structures and geometry of nonholonomic constraints
Dirac structures and geometry of nonholonomic constraints
Dirac structures and geometry of nonholonomic constraints
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Constrained Lagrangian system according to Y & M<br />
Let L : TQ → R be a Lagrangian (possibly not hyperregular).<br />
T∗TQ ζ<br />
⑤⑤⑤⑤⑤⑤⑤⑤⑤<br />
❆<br />
π ❆ TQ ❆<br />
<br />
T∗Q❇ TQ<br />
❇<br />
πQ τQ ❇<br />
<br />
⑥⑥⑥⑥⑥⑥⑥⑥⑥<br />
<br />
❲<br />
❆dL<br />
✮<br />
★<br />
❴<br />
❴ ❴ ❴ FL❴<br />
❴ ❴ ❴<br />
Q<br />
Definition<br />
The Legendre map FL : TQ → T ∗ Q is defined by the formula<br />
FL = ζ ◦ dL.<br />
KG (KMMF) Seminarium Geometryczne 13 X 2010 8 / 26
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