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d’Alembert–Lagrange analytical dynamics for nonholonomic systems
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10.1063/1.3559128
/content/aip/journal/jmp/52/3/10.1063/1.3559128
http://aip.metastore.ingenta.com/content/aip/journal/jmp/52/3/10.1063/1.3559128
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Physical states A(t) and B(t + dt) are perturbed to C and D′ under nonintegrable constraints. (a) Commutation rule (2.14) implies a continuous path CD of nonpossible displaced states C and D. (b) Noncommutation rule (4.6) implies two possible displaced states C and D′, but CD′ is discontinuous. The vector from D′ to D is δ(dq) − dq) in the nq-space. For integrable constraints, DD′ and DCABD′ closes at D′ to give continuous possible displaced states.

Image of FIG. 2.
FIG. 2.

The penny rolls upright while turning on an inclined plane of angle α. Directions of space-fixed axes are , and , as indicated. Disk rolls along the plane with angular velocity about symmetry axis which turns with constant angular velocity about fixed figure axis . The CM has velocity and the point of contact P is instantaneously at rest.

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/content/aip/journal/jmp/52/3/10.1063/1.3559128
2011-03-18
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: d’Alembert–Lagrange analytical dynamics for nonholonomic systems
http://aip.metastore.ingenta.com/content/aip/journal/jmp/52/3/10.1063/1.3559128
10.1063/1.3559128
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