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 />
Back<br />
We treat ∆ as a relation T ∗ T ∗ Q −− ⊲ TT ∗ Q<br />
We can take a ”short-cut” identifying T ∗ T ∗ Q with T ∗ TQ<br />
Local expressions:<br />
TT∗Q❊ T<br />
✡ TπQ ❊<br />
✡ ❊<br />
τT∗Q ✡<br />
✡<br />
✡<br />
✡<br />
∗ ˜∆ <br />
✤<br />
TQ <br />
dL<br />
✡<br />
❊<br />
❊<br />
ζ ✡ π ❊ TQ <br />
✡<br />
∆Q ✡ ∆Q<br />
✡<br />
✡<br />
T∗Q T∗Q T ∗ TO O × V × V ∗ × V ∗ ∋ (q, ˙q, c, d)<br />
TT ∗ O O × V ∗ × V × V ∗ ∋ (q, p, ˙q, ˙p)<br />
˜∆ : ˙q ∈ ∆Q(q), p = d ˙p − c ∈ ∆ ◦ Q (q)<br />
KG (KMMF) Seminarium Geometryczne 13 X 2010 16 / 26