相关论文: Quaternionic Hamilton equations
The so-called polynomial equations play an important role both in algebra and in the theory of functional equations. If the unknown functions in the equation are additive, relatively many results are known. However, even in this case, there…
The long-term evolution of astrophysical systems is driven by a Hamiltonian that is independent of the fast angle. As this Hamiltonian may contain explicitly time-dependent parameters, the conservation of mechanical energy is not guaranteed…
Quaternions, discovered by Sir William Rowan Hamilton in the 19th century, are a significant extension of complex numbers and a profound tool for understanding three-dimensional rotations. This work explores the quaternion's history,…
The quantization of classical theories that admit more than one Hamiltonian description is considered. This is done from a geometrical viewpoint, both at the quantization level (geometric quantization) and at the level of the dynamics of…
We derive the Hamiltonian function for extended teleparallel theories of gravity in their covariant formulation. In particular, we present the Hamiltonian for $f(T)$ gravity and New General Relativity. From this, we obtain the related…
We discuss a classical complexity of finite-dimensional unitary transformations, which can been seen as a computable approximation of classical descriptional complexity of a unitary transformation acting on a set of qubits.
For a non-relativistic particle subject to a Hamiltonian that is quadratic in position and momentum, with coefficients that may vary with time, it is shown that the effect of the linear terms in the Hamiltonian is just a spatial translation…
We consider a classical spinning particle in the frame of the relativistic physics by means of a covariant Hamiltonian and of a generalization of Poisson brackets which take into account the gauge fields. We obtain different equations of…
Classical Hamiltonian system of a point moving on a sphere of fixed radius is shown to emerge from the constrained evolution of quantum spin. The constrained quantum evolution corresponds to an appropriate coarse-graining of the quantum…
Lagrangian submanifolds are becoming a very essential tool to generalize and geometrically understand results and procedures in the area of mathematical physics. Here we use general Lagrangian submanifolds to provide a geometric version of…
Quaternion analysis is considered in full details where a new analyticity condition in complete analogy to complex analysis is found. The extension to octonions is also worked out.
We consider the problem of learning an interpretable potential energy function from a Hamiltonian system's trajectories. We address this problem for classical, separable Hamiltonian systems. Our approach first constructs a neural network…
It is shown that a given non-autonomous system of two first-order ordinary differential equations can be expressed in Hamiltonian form. The derivation presented here allow us to obtain previously known results such as the infinite number of…
The usual implement procedure for the reconstruction of secular equation for an effective Hamiltonian has been discussed and improved. A relative characteristic polynomial has been introduced for the effective Hamiltonian, to obtain a…
Quaternion analysis of time dependent Maxwell's equations in presence of electric and magnetic charges has been developed in unique, simple and consistent manner. It has been shown that this theory is extended consistently to time-harmonic…
The indefinite sign of the Hamiltonian constraint means that solutions to Einstein's equations must achieve a delicate balance--often among numerically large terms that nearly cancel. If numerical errors cause a violation of the Hamiltonian…
A generalization of classical mechanics is obtained from a complex parametrization of the phase space. The formalism supports complex Hamiltonian functions describing non-conservative classical mechanical systems. A quantization scheme that…
A general framework for the solutions of the constraints of pure gravity is constructed. It provides with well defined mathematical criteria to classify their solutions in four classes. Complete families of solutions are obtained in some…
The multiplicative Lagrangian and Hamiltonian introduce an additional parameter that, despite its variation, results in identical equations of motion as those derived from the standard Lagrangian. This intriguing property becomes even more…
With the modified Riemann-Liouville fractional derivative, a fractional Tu formula is presented to investigate generalized Hamilton structure of fractional soliton equations. The obtained results can be reduced to the classical Hamilton…