Lagrangian and Hamiltonian geometries. Applications to Mechanics

ISBN-13: 9783659710193 / Angielski / Miękka / 2015 / 260 str.

Miron Radu

Opis

The purpose of this book is to provide a presentation of the geometrical theory of Lagrange and Hamilton spaces of order k, greater or equal to 1, as well as to define and investigate some new Analytical Mechanics. It is shown that a rigorous geometrical theory of conservative and non-conservative mechanical systems can be raised based on the Lagrangian and Hamiltonian geometries. And that these geometries relies on the mechanical principles. The book covers the following topics : Lagrange and Hamilton spaces; Lagrange and Hamilton spaces of higher order; Analytical Mechanics of Lagrangian and Hamiltonian mechanical systems. The novelty consists of the following:a geometrization of the classical non-conservative mechanical systems, whose external forces depend on velocities, the notion of Finslerian mechanical system, the definition of Cartan mechanical system, a theory of Lagrangian and Hamiltonian mechanical systems by means of the geometry of tangent (cotangent) bundle, the geometrization of the higher order Lagrangian and Hamiltonian mechanical systems, fundamental equations of Riemannian mechanical systems whose external forces depend on higher order accelerations.

O autorze

Professor Radu MIRON Ph D (born on October 3, 1927 in Romania) has made many important contributions to Differential Geometry. He is a member of the Romanian Academy and doctor honoris causa of several universities. He published over 250 papers and 30 books and monographs. He introduced and studied the Lagrangian and Hamiltonian geometries.