Two non-holonomic integrable problems tracing back to Chaplygin
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The paper considers two new integrable systems which go back to Chaplygin. The systems consist of a spherical shell that rolls on a plane; within the shell there is a ball or Lagrange’s gyroscope. All necessary first integrals and an invariant measure are found. The solutions are shown to be expressed in terms of quadratures.
Keywordsnon-holonomic constraint integrability invariant measure gyroscope quadrature coupled rigid bodies
MSC2010 numbers76M23 34A05
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- 2.Chaplygin, S.A., On Some Generalization of the Area Theorem with Applications to the Problem of Rolling Balls, Regul. Chaotic Dyn., 2012, vol. 8, no. 2, pp. 199–217 [Russian original: Mat. Sb., 1897, Vol. 20; reprinted in: Collected Works: Vol. 1, Moscow-Leningrad: Gostekhizdat, 1948, pp. 26–56].CrossRefGoogle Scholar
- 3.Alves, J. and Dias, J., Design and Control of a Spherical Mobile Robot, J. Systems and Control Engineering, 2003, vol. 217, pp. 457–467.Google Scholar
- 4.Bhattacharya, S. and Agrawal, S.K., Design, Experiments and Motion Planning of a Spherical Rolling Robot, in Proc. of the IEEE Internat. Conf. on Robotics and Automation (San Francisco, CA, April 2000), IEEE, 2000, pp. 1207–1212.Google Scholar
- 7.Camicia, C., Conticelli, F., and Bicchi, A., Nonholonimic Kinematics and Dynamics of the Sphericle, in Proc. of the 2000 IEEE/RSJ Internat. Conf. on Intelligent Robots and Systems (Takamatsu, Japan, Oct. 31–Nov. 5 2000), IEEE, 2000, pp. 805–810.Google Scholar
- 8.Chung, W., Nonholonomic Manipulators, Springer Tracts in Advanced Robotics, vol. 13, Berlin: Springer, 2004.Google Scholar
- 9.Crossley, V.A., A Literature Review on the Design of Spherical Rolling Robots, Pittsburgh, PA, 2006.Google Scholar