Dissertation
Dissertation > Mathematical sciences and chemical > Mechanics > Theoretical Mechanics ( general mechanics ) > Analytical Mechanics ( analytical mechanics)

With expansion of the system when the binding study of symmetries of Newton's laws

Author LiZiYan
Tutor FuJingLi
School Zhejiang University of Technology
Course Basic mathematics
Keywords nonconservative system nonholonomic system extending Newton’s law Noether symmtry
CLC O316
Type Master's thesis
Year 2011
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Newton’s law of motion and the symmetry research of mechanical system have a extensive applicated field. Most problems from various practical background, with interdisciplinary characteristics, have vital importance both in theory and in practical application.In the natural sciences,no matter the Classical mechanics, Lagrange dynamics, Hamilton mechanics and Birkhoff mechanics or engineering technology areas, it’s convenient to use the method of Newton’s laws of motion and the symmetry to describe.Due to the importance and value of Newton’s laws of motion and symmetry research, this paper focuses on studying the equations of motion and symmetry of the time-dependent constraint mechanical system.The second chapter focus on studying extending Newton’s law from nonlocal-in-time kinetic energy of nonconservative dynamical systems.Application of the nonlocal-in-time kinetic energy, and high-order Lagrangian function,we study the extending Newton’s laws of motion and related theory of nonconservative system.In the third chapter,we deal with extending Newton’s law from nonlocal-in-time kinetic energy of non-holonomic dynamical systems.Application of the nonlocal-in-time kinetic energy, and high-order Lagrangian function,we do some research on the extending Newton’s laws of motion and related theory of nonholonomic systems.Based on these,we obtain a series of new properties and deduce the (1+1)-dimensional formalism of nonlocal theories based on Ostrogradski Hamiltonian canonical equation of the non-holonomic dynamical systems.The forth chapter focus on studying Noether symmetry and conserved quantity for time-dependent nonconservative systems.From the Hamilton under the infinitesimal point transformations’ unchanging properties of the time-dependent nonconservative system——the Noether symmetry,we obtain the Noether’s law of the nonconservative system.The novelty of this thesis consists in extending the extending Newton’s law from holonomic system to nonholonomic nonconservative systems,and obtains the correspondent Newton’s law and correspondent symmetries and invariant

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