@inbook{9451b257ebdd4dcdaaf5a67790d3d67d,

title = "The Role of the Jacobi Last Multiplier in Nonholonomic Systems and Locally Conformal Symplectic Structure",

abstract = "In this pedagogic article we study the geometrical structure of nonholonomic system and elucidate the relationship between Jacobi{\textquoteright}s last multiplier (JLM) and nonholonomic systems endowed with the almost symplectic structure. In particular, we present an algorithmic way to describe how the two form and almost Poisson structure associated to nonholonomic system, studied by L. Bates and his coworkers (Rep Math Phys 42(1–2):231–247, 1998; Rep Math Phys 49(2–3):143–149, 2002; What is a completely integrable nonholonomic dynamical system, in Proceedings of the XXX symposium on mathematical physics, Toru{\'n}, 1998; Rep Math Phys 32:99–115, 1993), can be mapped to symplectic form and canonical Poisson structure using JLM. We demonstrate how JLM can be used to map an integrable nonholonomic system to a Liouville integrable system. We map the toral fibration defined by the common level sets of the integrals of a Liouville integrable Hamiltonian system with a toral fibration coming from a completely integrable nonholonomic system.",

keywords = "Conformal Hamiltonian, Jacobi last multiplier, Liouville integrability, Nonholonomic system, Torus fibration",

author = "Partha Guha",

note = "Funding Information: Acknowledgements Most of the results herewith presented have been obtained in long-standing collaboration with Anindya Ghose Choudhury and Pepin Cari{\~n}ena, which is gratefully acknowledged. The author wishes also to thank Gerardo Torres del Castillo, Clara Nucci, Peter Leach, Debasish Chatterji, Ravi Banavar, and Manuel de Leon for many enlightening discussions. This work was done mostly while the author was visiting IHES. He would like to express his gratitude to the members of IHES for their warm hospitality. The final part was done at IFSC, USP at Sao Carlos and the support of FAPESP is gratefully acknowledged with grant number 2016/06560-6. Publisher Copyright: {\textcopyright} 2018, Springer Nature Switzerland AG.",

year = "2018",

doi = "10.1007/978-3-319-97175-9_12",

language = "British English",

series = "STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics and Health",

publisher = "Springer Nature",

pages = "275--291",

booktitle = "STEAM-H",

address = "United States",

}