Preface

Lagrangian mechanics is widely used in several areas of research and technology. It is sim‐ ply a reformulation of the classical mechanics by the mathematician and astronomer Joseph-Louis Lagrange in 1788. The approach formulates the physical phenomena through a function called Lagrangian, which is a function of generalized coordinates and contains the dynamics of the system through the derivatives.

Lagrangian mechanics is good for systems with conservative forces. If the dissipative forces are included, these forces should be separated into potential and nonpotential forces. This formulation gives a set of modified Euler-Lagrange equations. The user can choose general‐ ized coordinates such as the symmetries in the system or the geometry of the constraints. This may simplify the solutions for the motion of the system.

Lagrangian mechanics is also important for its role in deep understanding of physics be‐ sides its broad applications. It is applicable to most of the fundamental theoretical physics, such as quantum mechanics and relativity theory, even though Lagrange considered only the classical mechanics in *Mecanique Analytique*. Hamilton's principle is closely related to La‐ grangian mechanics, since it can be employed in the derivation of Lagrangian equations.

Lagrangian mechanics can also be applied to other systems. An example of these systems is the coupled electric circuit including inductive and capacitive components. Lagrangian me‐ chanics is a good alternative in solving mechanical problems in physics and engineering, especially when Newton's formulation of classical mechanics is not convenient. It can also be used in the optimization problems of dynamic systems.

In this book, the section authors provide state-of-the-art research studies on Lagrangian mechanics. Hopefully, the researchers will benefit from the book in their studies. It is probable that the presented studies may lead the researchers to develop new ideas in conducting their research.

> **Dr. Hüseyin Canbolat** Yildirim Beyazit University, Ankara, Turkey

**Section 1**
