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- W2029694480 abstract "In the present paper we consider a quite general problem of motion of a rigid body under the action of an axially symmetric combination of potential and gyroscopic forces. Special versions of this problem are the classical problems of motion of a heavy body, gyrostat or a body in a liquid. Another example is the problem of motion of a heavy, magnetized and electrically charged body under the combined action of gravitational, magnetic electric and Lorentz forces. We introduce a method, based on the invariance of the equations of motion under certain transformations. This method enables a systematic construction of several integrable problems generalizing all the known general (for arbitrary initial conditions) and conditional (on a single level of the cyclic integral) integrable problems as well as particular solutions. Five general integrable cases are constructed, that generalize known ones by the inclusion of one to four additional free parameters. Fifteen conditional integrable cases generalizing all the known general and conditional cases and containing an additional arbitrary function are introduced. The latter type of generalization can be applied to any one of a large collection of particular solutions known in many versions of the problem considered. The method also enables the construction of the explicit solutions of the equations of motion in the generalized cases from those of the original cases. Detailed physical interpretation is given for some cases." @default.
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- W2029694480 date "1999-10-13" @default.
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- W2029694480 title "New generalizations of all the known integrable problems in rigid-body dynamics" @default.
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- W2029694480 doi "https://doi.org/10.1088/0305-4470/32/43/309" @default.
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