Dynamical Equations, Invariants and Spectrum Generating Algebras of Mechanical Systems with Position-Dependent Mass [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2013 We analyze the dynamical equations obeyed by a classical system with position-dependent mass. It is shown that there is a non-conservative force quadratic in the velocity associated to the variable mass.
Sara Cruz y Cruz, Oscar Rosas-Ortiz
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What is liquid? Lyapunov instability reveals symmetry-breaking irreversibilities hidden within Hamilton's many-body equations of motion [PDF]
Condensed Matter Physics, 2015 Typical Hamiltonian liquids display exponential "Lyapunov instability", also called "sensitive dependence on initial conditions". Although Hamilton's equations are thoroughly time-reversible, the forward and backward Lyapunov instabilities can differ ...
Wm.G. Hoover, C.G. Hoover
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Hamiltonian Computational Chemistry: Geometrical Structures in Chemical Dynamics and Kinetics [PDF]
EntropyThe common geometrical (symplectic) structures of classical mechanics, quantum mechanics, and classical thermodynamics are unveiled with three pictures.
Stavros C. Farantos
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Mathematics, 2023 Because of the nonlocal and nonsingular properties of fractional derivatives, they are more suitable for modelling complex processes than integer derivatives.
Linli Wang, Jingli Fu, Liangliang Li
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Size-dependent Nonlinear Forced Vibration Analysis of Viscoelastic/Piezoelectric Nano-beam [PDF]
Journal of Applied and Computational Mechanics, 2021 In this paper, the nonlinear forced vibration of isotropic viscoelastic/ piezoelectric Euler-Bernoulli nano-beam is investigated. For this purpose, the consistent couple stress theory is utilized for modeling the viscoelastic/piezoelectric nano-beam ...
Zahra Tadi Beni +2 more
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‘Uncertainty’ principle in two fluid–mechanics [PDF]
ESAIM: Proceedings and Surveys, 2020 Hamilton’s principle (or principle of stationary action) is one of the basic modelling tools in finite-degree-of-freedom mechanics. It states that the reversible motion of mechanical systems is completely determined by the corresponding Lagrangian which ...
Gavrilyuk Sergey
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Long-term stability of cylindrical shells of viscoelastic composites
Lietuvos Matematikos Rinkinys, 2002 On the grounds of Hamilton's principle the system of linear integral equations has been obtained for the solution of stability problems of cylindrical shells made of viscoelastic composite materials by the finite element method.
Vaclovas Sirius
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Hamilton–Jacobi Equations [PDF]
, 2018 Hamilton–Jacobi equations are treated in the fifth chapter. Hamilton–Jacobi equations, their solutions, and the case of a time independent Hamiltonian are first recalled. Thirteen exercises are then solved, namely on a third harmonic oscillator, on a free falling particle, on a projectile ballistic flight, on a particle sliding on an inclined plane, on
Stanley Osher, Ronald Fedkiw
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Theory of Generalized Canonical Transformations for Birkhoff Systems
Advances in Mathematical Physics, 2020 Transformation is an important means to study problems in analytical mechanics. It is often difficult to solve dynamic equations, and the use of variable transformation can make the equations easier to solve. The theory of canonical transformations plays
Yi Zhang
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Exact solution for frequency equations of radial and transverse vibration of a circular plate with various boundary conditions [PDF]
مجله مدل سازی در مهندسی, 2017 In this study, closed-form relations are obtained for the frequency equations of radial (in-plane) and transverse (out-ofâplane) free vibration of a circular plate with free, simply-support, and clamped boundary conditions.
Mohammad Heidari-Rarani +2 more
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