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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Example<br />
Equations for a curve t ↦−→ (x(t), y(t), ϕ(t), px(t), py (t), π(t))<br />
˙x = px/m, ˙px = µ(t) sin ϕ<br />
˙y = py /m, ˙py = −µ(t) cos ϕ<br />
˙ϕ = π/m, ˙π = 0<br />
˙x sin ϕ = ˙y cos ϕ<br />
Solution (momentum)<br />
π(t) = π0<br />
px(t) = p0 cos( π0<br />
t + ϕ0)<br />
I<br />
py (t) = p0 sin( π0<br />
t + ϕ0)<br />
I<br />
KG (KMMF) Seminarium Geometryczne 13 X 2010 23 / 26