منابع مشابه
Supplement on Lagrangian, Hamiltonian Mechanics
⋆ When there are several independent variables it is easy to make mistakes in taking partial derivatives. The fundamental rule is: always know which set of independent variables is in use, so that you are sure which are being held fixed during the process of taking a partial derivative. ⋆ A simple example will illustrate the problems that await the careless. Start with f(x, y) = 2x + y; ∂f/∂x =...
متن کاملHamiltonian mechanics.
Comment on " Berry phase correction to electron density in solids " by Xiao et al. Abstract The main result of Xiao et al. In a recent paper on the semiclassical dynamics of a Bloch electron, Xiao, Shi and Niu [1] claim that, due to a Berry curvature term, Liouville's theorem on the conservation of the phase-space volume element would be violated, a fact which would have been overlooked so far....
متن کاملProgressive Damage Analysis of Laminated Composites using Continuum Damage Mechanics
In this paper, progressive damage and global failure of composite laminates under quasi-static, monotonic loading are investigated using 3D continuum damage mechanics. For this purpose, a finite element program has been developed using an eight-node 2D layered element including layer-wise plate theory. Damage analysis of a single orthotropic layer under various uniform in-plane and transverse l...
متن کاملThermal vibration analysis of double-layer graphene embedded in elastic medium based on nonlocal continuum mechanics
This paper presents the thermal vibration analysis of double-layer graphene sheet embedded in polymer elastic medium, using the plate theory and nonlocal continuum mechanics for small scale effects. The graphene is modeled based on continuum plate theory and the axial stress caused by the thermal effects is also considered. Nonlocal governing equations of motion for this double-layer graphene s...
متن کاملOn the Hamiltonian Description of Fluid Mechanics
We suggest the Hamiltonian approach for fluid mechanics based on the dynamics, formulated in terms of Lagrangian variables. The construction of the canonical variables of the fluid sheds a light on the origin of Clebsh variabes, introduced in the previous century. The develoted formalism permitts to relate the circulation conservation (Tompson theorem) with the invariance of the theory with res...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physica D: Nonlinear Phenomena
سال: 2020
ISSN: 0167-2789
DOI: 10.1016/j.physd.2020.132510