The constrained motion of a particle on an elliptical path is studied using Hamiltonian mechanics through Poisson bracket and Lagrangian mechanics through Euler Lagrange equation using non-natural Lagrangian. We calcu...The constrained motion of a particle on an elliptical path is studied using Hamiltonian mechanics through Poisson bracket and Lagrangian mechanics through Euler Lagrange equation using non-natural Lagrangian. We calculate the generalized momentum p<sub>θ</sub> and we find that this quantity is not conserved and the conjugate θ coordinate is not a cyclic coordinate.展开更多
The elliptic motion of particle in the fields of the inhomogeneous plane wavs that are generated on a liquid thermoviscoelastic solid interface is studied.. Calculations show that the ellipticity of the motion of Part...The elliptic motion of particle in the fields of the inhomogeneous plane wavs that are generated on a liquid thermoviscoelastic solid interface is studied.. Calculations show that the ellipticity of the motion of Particle is related to the incident angle that the homogeneous plane wave incidents upon the interface. The influeree of viscous properties of solid on the ellipticity of particle's motion is small and shows near the critical angles of longitudinal and transversal wavs. Under the incidence at Rayleigh angle, the change of the ellipticity of motion of the particle is periodic in the wake of its Rayleigh wavelength and its elliptic locus is couoter clockwise and clockwise rotation periodically.展开更多
文摘The constrained motion of a particle on an elliptical path is studied using Hamiltonian mechanics through Poisson bracket and Lagrangian mechanics through Euler Lagrange equation using non-natural Lagrangian. We calculate the generalized momentum p<sub>θ</sub> and we find that this quantity is not conserved and the conjugate θ coordinate is not a cyclic coordinate.
文摘The elliptic motion of particle in the fields of the inhomogeneous plane wavs that are generated on a liquid thermoviscoelastic solid interface is studied.. Calculations show that the ellipticity of the motion of Particle is related to the incident angle that the homogeneous plane wave incidents upon the interface. The influeree of viscous properties of solid on the ellipticity of particle's motion is small and shows near the critical angles of longitudinal and transversal wavs. Under the incidence at Rayleigh angle, the change of the ellipticity of motion of the particle is periodic in the wake of its Rayleigh wavelength and its elliptic locus is couoter clockwise and clockwise rotation periodically.
