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 />
A Lagrangian system with <strong>nonholonomic</strong> <strong>constraints</strong> ∆Q can be described<br />
by a triple<br />
(L, ∆, X )<br />
where<br />
L is a Lagrangian function, possibly not hyperregular,<br />
∆ is the <strong>Dirac</strong> structure associated to the constraint distribution ∆Q,<br />
X is a partial vector field defined in points<br />
<strong>and</strong> such that<br />
(v, p) ∈ TQ ⊕ T ∗ Q, such that v ∈ ∆Q, p = FL(v)<br />
X (v, p) + DL(v) ∈ ∆<br />
KG (KMMF) Seminarium Geometryczne 13 X 2010 12 / 26
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