Dirac structures and geometry of nonholonomic constraints

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My point of view The unconstrained case: all virtual displacements are admissible KG (KMMF) Seminarium Geometryczne 13 X 2010 18 / 26
My point of view The constrained case: we choose admissible displacements Locally: U = {u ∈ TTQ : τTQ(u) ∈ ∆Q, TτQ(u) ∈ ∆Q} u = (q, ˙q, δq, δ ˙q) : ˙q ∈ ∆Q(q), δq ∈ ∆Q(q) κQ(U) = U We treat κQ |U as a relation in TTQ and we look for the dual relation with respect to the evaluations 〈·, ·〉, 〈〈·, ·〉〉. KG (KMMF) Seminarium Geometryczne 13 X 2010 19 / 26
Page 1 and 2: Dirac structures and geometry of no
Page 3 and 4: Introduction References Hiroaki Yos
Page 5 and 6: Contents Dirac structure Dirac stru
Page 11 and 12: Dirac structure Definition A Dirac
Page 13 and 14: Almost Dirac structure in mechanics
Page 19 and 20: Almost Dirac structures in mechanic
Page 25 and 26: Constrained Lagrangian system accor
Page 35 and 36: My point of view Lagrangian dynamic
Page 37 and 38: My point of view Back We treat ∆
Page 39 and 40: My point of view Back We treat ∆
Page 41 and 42: My point of view How to get ˜ ∆
Page 43 and 44: My point of view How to get ˜ ∆
Page 45: My point of view How to get ˜ ∆
Page 49 and 50: My point of view The constrained ca
Page 51 and 52: My point of view ˜∆ KG (KMMF) Se
Page 53 and 54: My point of view Conclusion The rel
Page 55 and 56: Example Equations for a curve t ↦
Page 57 and 58: Example Initial momentum along the

Dirac structures and geometry of nonholonomic constraints

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