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- Falling_cat_problem abstract "The falling cat problem consists of explaining the underlying physics behind the common observation of the cat righting reflex: how a free-falling cat can turn itself right-side-up as it falls, no matter which way up it was initially, without violating the law of conservation of angular momentum.Although somewhat amusing, and trivial to pose, the solution of the problem is not as straightforward as its statement would suggest. The apparent contradiction with the law of conservation of angular momentum is resolved because the cat is not a rigid body, but instead is permitted to change its shape during the fall. The behavior of the cat is thus typical of the mechanics of deformable bodies.The solution of the problem, originally due to (Kane & Scher 1969), models the cat as a pair of cylinders (the front and back halves of the cat) capable of changing their relative orientations. Montgomery (1993) later described the Kane–Scher model in terms of a connection in the configuration space that encapsulates the relative motions of the two parts of the cat permitted by the physics. Framed in this way, the dynamics of the falling cat problem is a prototypical example of a nonholonomic system (Batterman 2003), the study of which is among the central preoccupations of control theory. A solution of the falling cat problem is a curve in the configuration space that is horizontal with respect to the connection (that is, it is admissible by the physics) with prescribed initial and final configurations. Finding an optimal solution is an example of optimal motion planning (Arbyan & Tsai 1998; Ge & Chen 2007).In the language of physics, Montgomery's connection is a certain Yang-Mills field on the configuration space, and is a special case of a more general approach to the dynamics of deformable bodies as represented by gauge fields (Montgomery 1993; Batterman 2003), following the work of Shapere and Wilczek (Shapere and Wilczek 1987).".
- Falling_cat_problem thumbnail Cat_fall_150x300_6fps.gif?width=300.
- Falling_cat_problem wikiPageExternalLink marsden1.html.
- Falling_cat_problem wikiPageExternalLink montgomery.html.
- Falling_cat_problem wikiPageID "21477359".
- Falling_cat_problem wikiPageRevisionID "606138797".
- Falling_cat_problem hasPhotoCollection Falling_cat_problem.
- Falling_cat_problem subject Category:Biophysics.
- Falling_cat_problem subject Category:Cat_behavior.
- Falling_cat_problem subject Category:Classical_mechanics.
- Falling_cat_problem subject Category:Control_theory.
- Falling_cat_problem subject Category:Rotation.
- Falling_cat_problem comment "The falling cat problem consists of explaining the underlying physics behind the common observation of the cat righting reflex: how a free-falling cat can turn itself right-side-up as it falls, no matter which way up it was initially, without violating the law of conservation of angular momentum.Although somewhat amusing, and trivial to pose, the solution of the problem is not as straightforward as its statement would suggest.".
- Falling_cat_problem label "Falling cat problem".
- Falling_cat_problem label "مسألة سقوط القط".
- Falling_cat_problem sameAs m.05h4scv.
- Falling_cat_problem sameAs Q5432366.
- Falling_cat_problem sameAs Q5432366.
- Falling_cat_problem wasDerivedFrom Falling_cat_problem?oldid=606138797.
- Falling_cat_problem depiction Cat_fall_150x300_6fps.gif.
- Falling_cat_problem isPrimaryTopicOf Falling_cat_problem.
