Complete list of first integrals of dynamic equations of motion of a 4D rigid body in a nonconservative field under the assumption of linear damping
The dynamic part of equations of motion of a dynamically symmetric 4D rigid body, where the force field is concentrated on that part of the body that has the form of a two-dimensional disc, is investigated. In this case, the tensor of the angular velocity of such a body is six-dimensional, while the velocity of the center of mass is four-dimensional. Under certain conditions, a complete list of first integrals, which are expressed through elementary functions, is obtained.
KeywordsForce Field Resistance Force Dynamic Part Variable Dissipation Doklady Phys
Unable to display preview. Download preview PDF.
- 5.M. V. Shamolin, Vestn. Mosk. Gos. Univ., Ser. 1: Mat. Mekh., No. 1, 52 (1992).Google Scholar
- 6.M. V. Shamolin, Methods of Analysis of Dynamic Systems with a Variable Dissipation in Rigid-Body Dynamics (Ekzamen, Moscow, 2007) [in Russian].Google Scholar
- 8.V. V. Trofimov and A. T. Fomenko, Algebra and Geometry of Integrable Hamilton Differential Equations (Faktorial, Moscow, 1995) [in Russian].Google Scholar
- 11.S. A. Chaplygin, in Complete Works (AN SSSR, Leningrad, 1933), Vol. 1, pp. 133–135 [in Russian].Google Scholar