We present a direct approach to the construction of Lagrangians for a large class of one-
dimensional dynamical systems with a simple dependence (monomial or polynomial) on the …

We present a method devised by Jacobi to derive Lagrangians of any second-order
differential equation: it consists in finding a Jacobi Last Multiplier. We illustrate the easiness …

We use a formula derived almost seventy years ago by Madhav Rao connecting the Jacobi
Last Multiplier of a second-order ordinary differential equation and its Lagrangian and …

We exploit the relationships between the Lie symmetries of a mechanical system, the Jacobi
Last Multiplier and the Lagrangian of the system to construct alternative Lagrangians and …

In a recent paper by Ibragimov a method was presented in order to find Lagrangians of
certain second-order ordinary differential equations admitting a two-dimensional Lie …

The space of null Lagrangians is the least investigated territory in dynamics as these
Lagrangians are identically sent to zero by their Euler–Lagrange operator, and thereby they …

A set of linear second‐order differential equations is converted into a semigroup, whose
algebraic structure is used to generate novel equations. The Lagrangian formalism based …

The problem of obtaining canonical Hamiltonian structures from the equations of motion,
without any knowledge of the action, is studied in the context of the spatially flat …

Bertrand theorem's states that, among central-force potentials with bound orbits, there are
only two types of central-force scalar potentials with the property that all bound orbits are …

In this paper, we examine the role of the Jacobi last multiplier in the context of two-
dimensional oscillators. We first consider two-dimensional unit-mass oscillators admitting a …