相关论文: A methodology for formulating dynamical equations …
Elastodynamic equations have been formulated with either Newton's second law of motion, Lagrange's equation, or Hamilton's principle for over 150 years. In this work, contrary to classical continuum mechanics, a novel strategic methodology…
A conventional derivation of motion equations in mechanics and field equations in field theory is based on the principle of least action with a proper Lagrangian. With a time-independent Lagrangian, a function of coordinates and velocities…
A methodology is proposed for formulating dynamic equations in thermo-piezoelectric and dissipative media from the first principle of energy conservation. The results are in agreement with those from Hamiltonian principle. Our formulations…
The classical Lagrange formalism is generalized to the case of arbitrary stationary (but not necessarily conservative) dynamical systems. It is shown that the equations of motion for such systems can be derived in the standard ways from the…
From a new perspective, this paper rederives Lagrange's equations. By applying the chain rule of differentiation, the intrinsic relationship between the momentum theorem and the kinetic energy theorem is first established. Subsequently,…
We discuss a recently proposed variational principle for deriving the variational equations associated to any Lagrangian system. The principle gives simultaneously the Lagrange and the variational equations of the system. We define a new…
It is demonstrated that energy conservation allows for a straight derivation of Newtonian mechanics without an apriori definition of the concept of work. Furthermore it is shown that energy must be depicted as a function of position and…
Most classical mechanical systems are based on dynamical variables whose values are real numbers. Energy conservation is then guaranteed if the dynamical equations are phrased in terms of a Hamiltonian function, which then leads to…
A simple procedure is presented to study the conservation of energy equation with dissipation in continuum mechanics in 1D. This procedure is used to transform this nonlinear evolution-diffusion equation into a hyperbolic PDE; specifically,…
Hamilton's principle of stationary action lies at the foundation of theoretical physics and is applied in many other disciplines from pure mathematics to economics. Despite its utility, Hamilton's principle has a subtle pitfall that often…
We introduce a data-driven method for learning the equations of motion of mechanical systems directly from position measurements, without requiring access to velocity data. This is particularly relevant in system identification tasks where…
A longstanding open question in classical mechanics is to formulate the least action principle for dissipative systems. In this work, we give a general formulation of this principle by considering a whole conservative system including the…
In this paper, we develop a Hamiltonian variational formulation for the nonequilibrium thermodynamics of simple adiabatically closed systems that is an extension of Hamilton's phase space principle in mechanics. We introduce the…
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. We construct the Lagrangian and the…
It is most common to construct the Hamiltonian function and Hamilton's canonical equations through a Legendre transformation of the Lagrangean function or through the central equation. These common perspectives, however, seem abstract and…
In this paper we proposed a proposition: for any nonconservative classical mechanical system and any initial condition, there exists a conservative one; the two systems share one and only one common phase curve; the Hamiltonian of the…
Analytical (rational) mechanics is the mathematical structure of Newtonian deterministic dynamics developed by D'Alembert, Langrange, Hamilton, Jacobi, and many other luminaries of applied mathematics. Diffusion as a stochastic process of…
The usual canonical Hamiltonian or Lagrangian formalism of classical mechanics applied to macroscopic systems describes energy conserving adiabatic motion. If irreversible diabatic processes are to be included, then the law of increasing…
Recently the Hamilton-Jacobi formulation for first order constrained systems has been developed. In such formalism the equations of motion are written as total differential equations in many variables. We generalize the Hamilton-Jacobi…
Atmospheric systems incorporating thermal dynamics must be stable with respect to both energy and entropy. While energy conservation can be enforced via the preservation of the skew-symmetric structure of the Hamiltonian form of the…