Quasi-canonicalization for linear homogeneous nonholonomic systems

For conservative linear homogeneous nonholonomic systems, there exists a cotangent bundle with the symplectic structure dπ^μ∧dξ_μ, in which the motion equations of the system can be written into the form of the canonical equations by the set of quasi-coordinates π^μ and quasi-momenta ξ_μ. The key to construct this cotangent bundle is to define a set of suitable quasi-coordinates π^μ by a first-order linear mapping, so that the reduced configuration space of the system is a Riemann space with no torsion. The Hamilton-Jacobi method for linear homogeneous nonholonomic systems is studied as an application of the quasi-canonicalization. The Hamilton-Jacobi method can be applied not only to Chaplygin nonholonomic systems, but also to non-Chaplygin nonholonomic systems. Two examples are given to illustrate the effectiveness of the quasi-canonicalization and the Hamilton-Jacobi method.