Related papers: Topics on Hamiltonian Mechanics
Hamiltonian mechanics describes the evolution of a system through its Hamiltonian. The Hamiltonian typically also represents the energy observable, a Noether-conserved quantity associated with the time-invariance of the law of evolution. In…
We described the $q$-deformed phase space. The $q$-deformed Hamilton eqations of motion are derived and discussed. Some simple models are considered.
Further formulas are presented involving quantum mechanics, thermodynamics, and integrable systems. Modifications of dispersionless theory are developed.
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…
A sharper formulation is presented for an interpretation of quantum mechanics advocated by author. As an essential element we put forward conservation laws concerning the ontological nature of a variable, and the uncertainties concerning…
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…
Standandard Hamiltonian mechanics in its homogeneous formulation is applied to the study of discontinuities representing rapid changes of Hamiltonians. Different formulations of Hamiltonian mechanics are reviewed. An original representation…
We study some mechanical problems in which a friction force is acting on the system. Using the fundamental concepts of state, time evolution and energy conservation we explain how to extend Newtonian mechanics to thermodynamics. We arrive…
The goal of this study is to present quaternion Kaehler analogue of Hamiltonian mechanics. Finally, the some results related to quaternion Kaehler dynamical systems were also given.
First, Second and Combined Laws of Thermodynamics are revised in terms of entropy change, partial entropy, partial volume, and chemical potential.
We raise fundamental questions about the very meaning of conservation laws in quantum mechanics and we argue that the standard way of defining conservation laws, while perfectly valid as far as it goes, misses essential features of nature…
We discuss the key role that Hamiltonian notions play in physics. Five examples are given that illustrate the versatility and generality of Hamiltonian notions. The given examples concern the interconnection between quantum mechanics,…
Conservation laws are discussed in conjunction with quantum-mechanical indeterminacies of the corresponding observables. The considered examples show that the connections between energy and its indeterminacy may be quite intricate. The…
Using a theorem of partial differential equations, we present a general way of deriving the conserved quantities associated with a given classical point mechanical system, denoted by its Hamiltonian. Some simple examples are given to…
This study introduces standard Cliffordian Kaehler analogue of Hamiltonian mechanic systems. In the end, the some results related to standard Cliffordian Kaehler dynamical systems are also discussed.
A conceptually simple physical interpretation of a conserved Hamiltonian $\mathcal{H}$ for a mechanical system with a time-dependent constraint is given. For the case of a bead on a vertical hoop forced to rotate with constant angular…
We give a modified Hamiltonian for a particle in a box with infinite potential walls that takes into account wall effects. The Hamiltonian is expressed in both the position and momentum representation. In the momentum representation the…
We put forth the idea that Hamilton's equations coincide with deterministic and reversible evolution. We explore the idea from five different perspectives (mathematics, measurements, thermodynamics, information theory and state mapping) and…
A fractional Hamiltonian formalism is introduced for the recent combined fractional calculus of variations. The Hamilton-Jacobi partial differential equation is generalized to be applicable for systems containing combined Caputo fractional…
A derivation of the Bohm model, and some general comments about it, are given. A modification of the model which is formally local and Lorentz-invariant is introduced, and its properties studied for a simple experiment.