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 />
Conclusion<br />
The relation ˜∆ is dual to the relation κQ restricted to the set <strong>of</strong> admissible<br />
virtual displacements.<br />
Equations<br />
The equations for a curve t ↦−→ ℘(t) in the phase space T ∗ Q are<br />
Local expressions:<br />
t ↦−→ (q(t), p(t))<br />
t℘(t) ∈ ˜ ∆ ◦ dL(∆Q)<br />
˙q ∈ ∆Q(q(t)), p(t) = ∂L<br />
∂L<br />
(q, ˙q), ˙p(t) ∈<br />
∂ ˙q ∂q (q, ˙q) + ∆◦Q (q(t))<br />
KG (KMMF) Seminarium Geometryczne 13 X 2010 21 / 26