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 />
Definition<br />
For L : TQ → R the composition<br />
γQ ◦ dL : TQ −→ T ∗ T ∗ Q<br />
will be called the <strong>Dirac</strong> differential <strong>of</strong> L <strong>and</strong> denoted by DL<br />
Locally:<br />
DL(q, ˙q) = (q, ∂L<br />
, −∂L , ˙q)<br />
∂ ˙q ∂q<br />
KG (KMMF) Seminarium Geometryczne 13 X 2010 10 / 26