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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My point <strong>of</strong> view<br />
Lagrangian dynamics without <strong>constraints</strong> according to Y & M (when we<br />
forget partial vector fields)<br />
γQ<br />
T∗T∗Q● TT<br />
✟ ●ξ<br />
✟ ●<br />
πT∗Q ✟<br />
✟<br />
✟<br />
✟<br />
∗ αQ <br />
Q ❴ ❴ ❴ ❴ ❴ ❴ ❴ ❴ <br />
β ✡<br />
❋ TπQ ❋<br />
✡ ❋<br />
τT∗Q ✡<br />
✡<br />
✡<br />
✡<br />
−1<br />
T<br />
Q<br />
∗ <br />
TQ <br />
dL<br />
✡<br />
❋<br />
❋<br />
ζ ✡ π ❋<br />
TQ <br />
TQ<br />
TQ<br />
✡<br />
✡ TQ<br />
✡<br />
☛ ✡ ☛<br />
τQ ✡ τQ ☛ ✡<br />
☛<br />
✡ ☛ τQ<br />
T<br />
☛<br />
✡ ☛ ☛<br />
✡ ☛ ☛<br />
✡<br />
☛<br />
☛<br />
∗Q❍ T<br />
πQ ❍<br />
❍<br />
∗Q● T<br />
πQ ●<br />
●<br />
∗Q● πQ ●<br />
●<br />
Q Q Q<br />
DL = β −1<br />
Q (γQ(dL(TQ)))<br />
KG (KMMF) Seminarium Geometryczne 13 X 2010 13 / 26
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