Related papers: Introduction to Higher Order Classical Dynamics: P…
The aim of the present text is twofold: to provide a compendium of Lagrangian and Hamiltonian geometries and to introduce and investigate new analytical Mechanics: Finslerian, Lagrangian and Hamiltonian. The fundamental equations (or…
We discuss an elementary derivation of variational symmetries and corresponding integrals of motion for the Lagrangian systems depending on acceleration. Providing several examples, we make the manuscript accessible to a wide range of…
Different routes towards the canonical formulation of a classical theory result in different canonically equivalent Hamiltonians, while their quantum counterparts are related through appropriate unitary transformation. However, for…
In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…
Classical geometric mechanics, including the study of symmetries, Lagrangian and Hamiltonian mechanics, and the Hamilton-Jacobi theory, are founded on geometric structures such as jets, symplectic and contact ones. In this paper, we shall…
In order to derive a large set of Hamiltonian dynamical systems, but with only first order Lagrangian, we resort to the formulation in terms of Lagrange-Souriau 2-form formalism. A wide class of systems derived in different phenomenological…
We review a perturbative approach to deal with Lagrangians with higher or infinite order time derivatives. It enables us to construct a consistent Poisson structure and Hamiltonian with only first time derivatives order by order in…
An alternative version of Hamiltonian formalism for higher-derivative theories is presented. It is related to the standard Ostrogradski approach by a canonical transformation. The advantage of the approach presented is that the Lagrangian…
Dynamics of classical spinning particle in special relativity with Pirani constraint is a typical example of the generalized Hamilton theory developed by O. Krupkov\'a and discovers some characteristic features of the latter.
In this Thesis we develop the geometric formulations for higher-order autonomous and non-autonomous dynamical systems, and second-order field theories. In all cases, the physical information of the system is given in terms of a Lagrangian…
We perform a Hamiltonian analysis of a large class of scalar-tensor Lagrangians which depend quadratically on the second derivatives of a scalar field. By resorting to a convenient choice of dynamical variables, we show that the Hamiltonian…
We observe that a wide class of higher-derivative systems admits a bounded integral of motion that ensures the classical stability of dynamics, while the canonical energy is unbounded. We use the concept of a Lagrange anchor to demonstrate…
The k-cosymplectic Lagrangian and Hamiltonian formalisms of first-order field theories are reviewed and completed. In particular, they are stated for singular and almost-regular systems. Subsequently, several alternative formulations for…
The Hamiltonian formulation plays the essential role in constructing the framework of modern physics. In this paper, a new form of canonical equations of Hamilton with the complete symmetry is obtained, which are valid not only for the…
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…
Based on the results in [Nucl. Phys. B 866 (2013) 212], we consider a way to construct a higher-derivative mechanical model which possesses the $l$-conformal Galilei symmetry. The dynamical system describes generalized Pais-Uhlenbeck…
The focus of the thesis is to obtain a universal formalism to evaluate the perturbations during inflation at all orders that can be applied to any theory of gravity and matter source in the early universe. We first look at the equivalence…
We investigate the cosmological dynamics of scalar fields governed by higher-order gravity, with particular emphasis on models inspired by the Pais-Uhlenbeck oscillator--a prototypical fourth-order system known for its connection to…
A generalized canonical form of action of dynamic theories with higher derivatives is proposed, which does not require the introduction of additional dynamic variables. This form is the initial point for the construction of quantum theory,…
A calculation is presented that shows that Feynman's path integral implies Ostrogradsky's Hamiltonian for nonsingular Lagrangians with second derivatives. The procedure employs the stationary phase approximation to obtain the limiting…