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 />
There exists the canonical isomorphism<br />
Locally for O ⊂ Q we have<br />
<strong>and</strong><br />
γQ : T ∗ TQ −→ T ∗ T ∗ Q<br />
T ∗ TO O × V × V ∗ × V ∗ , T ∗ T ∗ O O × V ∗ × V ∗ × V<br />
γQ(q, ˙q, c, d) = (q, d, −c, ˙q)<br />
It exists for any vector bundle (not only tangent bundle), it is a double<br />
vector bundle isomorphism <strong>and</strong> antisymplectomorphism.<br />
KG (KMMF) Seminarium Geometryczne 13 X 2010 9 / 26
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