Mathematics is integral to understanding the science of nature, particularly in mechanics, which is the foundational science expressed through mathematical models. The interplay between mechanics and mathematics is highlighted, showing how mathematical tools have advanced the study of natural phenomena while also leading to the evolution of various mathematical concepts. This exploration emphasizes the reciprocal influence between these two fields, showcasing their collaborative development.
Focusing on analytical mechanics, this volume delves into advanced topics such as Lagrangian and Hamiltonian mechanics, along with the Hamilton-Jacobi method. It also explores systems with separate variables, providing a comprehensive understanding of these complex concepts within the field.
Focusing on classical elasticity theory, this comprehensive work delves into the intricate nature of deformable solids, a subject that poses challenges for computer modeling. Authored by a leading expert in the field, it serves as an extensive resource for understanding the complexities involved in elasticity and solid mechanics.
Volume II: Mechanics of Discrete and Continuous Systems
Focusing on the science of mechanics, this volume explores its fundamental principles and their significance in understanding natural phenomena. It emphasizes the application of these principles in engineering and problem-solving, making it an essential resource for students and professionals in the field.
Focusing on analytical mechanics, this final volume delves into advanced topics such as Lagrangian and Hamiltonian mechanics, alongside the Hamilton-Jacobi method. It also explores systems with separate variables, providing a comprehensive understanding of these complex concepts in the field of mechanics.
In this comprehensive monograph, the authors apply modern mathematical methods to the study of mechanical and physical phenomena or techniques in acoustics, optics, and electrostatics, where classical mathematical tools fail. They present a general method of approaching problems, pointing out different aspects and difficulties that may occur. With respect to the theory of distributions, only the results and the principle theorems are given as well as some mathematical results. The book also systematically deals with a large number of applications to problems of general Newtonian mechanics, as well as to problems pertaining to the mechanics of deformable solids and physics. Special attention is placed upon the introduction of corresponding mathematical models. Stress is put on the unified presentation of continuous and discontinuous phenomena. Addressed to a wide circle of readers who use mathematical methods in their work: applied mathematicians, engineers in various branches, as well as physicists, while also benefiting students in various fields.