Mechanics

This introduction to classical mechanics and thermodynamics provides an accessible and clear treatment of the fundamentals. Starting with particle mechanics and an early introduction to special relativity this textbooks enables the reader to understand the basics in mechanics. The text is written from the experimental physics point of view, giving numerous real life examples and applications of classical mechanics in technology.

The basics of Fluid Mechanics

This textbook teaches classical mechanics as one of the foundations of physics. It describes the mechanical stability and motion in physical systems ranging from the molecular to the galactic scale.
Aside from the standard topics of mechanics in the physics curriculum, this book includes an introduction to the theory of elasticity and its use in selected modern engineering applications, e.g. dynamic mechanical analysis of viscoelastic materials. The text also covers many aspects of numerical mechanics, ranging from the solution of ordinary differential equations, including molecular dynamics simulation of many particle systems, to the finite element method. Attendant Mathematica programs or parts thereof are provided in conjunction with selected examples. Numerous links allow the reader to connect to related subjects and research topics.

This text describes the mathematical formulation and proof of the unified mechanics theory (UMT) which is based on the unification of Newton’s laws and the laws of thermodynamics. It also presents formulations and experimental verifications of the theory for thermal, mechanical, electrical, corrosion, chemical and fatigue loads, and it discusses why the original universal laws of motion proposed by Isaac Newton in 1687 are incomplete.

This textbook aims at introducing readers, primarily students enrolled in undergraduate Mathematics or Physics courses, to the topics and methods of classical Mathematical Physics, including Classical Mechanics, its Lagrangian and Hamiltonian formulations, Lyapunov stability, plus the Liouville theorem and the Poincaré recurrence theorem among others. The material also rigorously covers the theory of Special Relativity. The logical-mathematical structure of the physical theories of concern is introduced in an axiomatic way, starting from a limited number of physical assumptions. Special attention is paid to themes with a major impact on Theoretical and Mathematical Physics beyond Analytical Mechanics, such as the Galilean symmetry of classical Dynamics and the Poincaré symmetry of relativistic Dynamics, the far-fetching relationship between symmetries and constants of motion, the coordinate-free nature of the underpinning mathematical objects, or the possibility of describing Dynamics in a global way while still working in local coordinates.

The fundamental questions arising in mechanics are: Why?, How?, and How much? The aim of this series is to provide lucid accounts written by authoritative researchers giving vision and insight in answering these questions on the subject of mechanics as it relates to solids.

As any human activity needs goals, mathematical research needs problems -David Hilbert Mechanics is the paradise of mathematical sciences -Leonardo da Vinci Mechanics and mathematics have been complementary partners since Newton's time and the history of science shows much evidence of the ben­ eficial influence of these disciplines on each other.

This textbook explores the theory of Cosserat continuum mechanics, and covers fundamental tools, general laws and major models, as well as applications to the mechanics of granular media. While classical continuum mechanics is based on the axiom that the stress tensor is symmetric, theories such as that expressed in the seminal work of the brothers Eugène and François Cosserat are characterized by a non-symmetric stress tensor.