This textbook introduces the field of mechanics, commonly offered at universities in Germany as part of structured courses in theoretical physics.
Within the framework of elementary Newtonian mechanics, the basic concepts — such as trajectory curves, mass point, equations of motion, reference frames — are introduced. The focus is placed on the Lagrangian formalism (Lagrangian equations of the first and second kind, Hamilton's principle, conservation laws, Noether's theorem, etc.) and its most important applications (e.g.: motion in a central potential, dynamics of a rigid body and harmonic oscillations). The Hamilton formalism is then introduced in a compact way and continuum mechanics is presented through illustrative examples, such as string vibrations, beam bending, elementary hydrodynamics, sound waves, and more. The book also deals in detail with special relativity (principle of relativity by Einstein, length contraction, time dilation, relativistic equation of motion, production of heavy particles, twin paradox, etc.), and is supplemented with an appendix that examines the relation between the Newtonian force and the Minkowksi force.
Contents:

Preface

Introduction

Elementary Newtonian Mechanics:

Trajectory

Newton's Laws

Conservation Laws

System of Mass Points

Inertial Frames

Accelerated Reference Frames

Lagrangian Formalism:

Lagrange's Equations of First Kind

Applications I

Lagrange's Equations Second Kind

Applications II

Space–Time Symmetries

Variational Principles:

Variation without Constraint

Variation with Constraint

Hamilton's Principle

Noether's Theorem

Central Potential:

Two-Body Problem

Kepler Problem

Scattering

Rigid Body:

Kinematics

Inertia Tensor

Tensors

Euler's Equations

Heavy Gyroscope

Small Oscillations:

Forced Oscillations

System with Many Degrees of Freedom

Applications

Hamiltonian Formalism:

Canonical Equations

Canonical Transformations

Hamilton–Jacobi Equation

Continuum Mechanics:

String Vibration

Beam Bending

Hydrodynamics

Field Theories

Relativistic Mechanics:

Relativity Principle

Length and Time Measurement

Lorentz Group

Lorentz Tensor

Equation of Motion

Applications

Lagrange Function

Newtonian Force and Minkowski Force

Index

Readership: Undergraduates in physics and engineering.
Key Features:

Successful German version (Springer), currently available in 8th edition

Very positive feedback from students and professors

Concise, compact and comprehensible presentation of the contents

The approach is more intuitive instead of deductive

Chapters are coherent, which allows focus on selective areas if desired

Especially clear-cut introduction of the Lagrangian formalism

Introduction into variational calculus (including examples like brachistochrone or catenary), leading eventually to Noether's theorem

Introduction to continuum mechanics via illustrative examples (like sting vibrations, beam bending, sound waves). Thereby, the basic concepts of field theories are presented

Thorough and clear-cut introduction to the theory of Special Relativity

The present edition is enriched by a clear and detailed discussion of the correct relation between the Newtonian force and the Minkowski force. The author gives the formal derivation of the correct relation and discusses the practical and logical relevance of the different statements in the literature