Rotational Motion and Poisson Bracket Structures in Rigid Particle Systems and Anisotropic Fluid Theory

摘要: We explore the origins of rotational motion in anisotropic fluid theories from most fundamental perspectives possible: collections discrete entities or continuous spectra particles which are allowed to translate and rotate simultaneously. In either case, starting point our analysis is principle least action applied rigid body systems involving both translation rotation. Our methods analyzing this problem very old recent, we hope that net result these an injection much originality into problem. Hamiltonian mechanics a system considered where explicit accounting made translational particle motion. The extended Poisson bracket written down terms appropriate generalized coordinates Hamiltonian system. A similar treatment quasi-coordinates also presented. An alternative formulation two orthogonal unit vectors offered simplifies mathematical description by working inertial reference frame with constant, diagonal inertia tensors. This methodology transferred continuum material functional relationships Volterra differentiation. analogous derived, ultimately spatial description, along Hamiltonian. results derivation general form ideal equations variables, important subcase Leslie-Ericksen theory liquid crystals. It extends provides insight molecular various constitutive (such as tensor, force, couple, etc.). motivation provide, based on structure for all different descriptions rotation, priori corresponding described leads their consistent generalization.