Fundamentals of classical and analytical mechanics

Lipiński Krzysztof

ISBN/ISSN: 978-83-7348-831-1

Issue: 1

Year published: 2021

Number of pages: 324

Tags: simplified theory of gyroscope, Lagrange proposed reformulation of mechanics, theory of vectors, kinematics of particles, dynamics of particles, spherical and general motion of rigid bodies



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The primary intention of Author of the present book was to draw up a monographic picture of the contemporary attempts used to describe the Newtonian and Lagrangian Mechanics. But concurrently, the book can be recognized as a supplementary educational material, useful for the graduate courses in Mechanics taken by students majoring in Mechanical Engineering, Civil Engineering or Physical Science.

A short synopsis of the subsequent chapters follows:

  1. Few words of introduction focusing on the domain, branches and the primary assumptions of mechanics;
  2. A brief introduction to the fundamental concepts and principles of algebra of vectors;
  3. Kinematics of particles, mainly focused on non-Cartesian coordinates used in mathematical descriptions of kinematics;
  4. Dynamics of particles; focused on Newton’s laws of motion; motion of particles in one and in three dimensions; dynamics expressed in inertial and non-inertial frames of reference; the principles of linear momentum and of angular momentum of particle; work and energy principles;
  5. Chapter 5. Kinematics and dynamics of spherical motion of rigid bodies; Euler’s angles; angular velocities and angular accelerations; conical surfaces of angular velocity vectors, steady precession, angular momentum of bodies in their spherical motion, Euler’s equations of dynamics for bodies in their spherical motion; kinetic energy formulae;
  6. Kinematics and dynamics of general motion of rigid bodies; linear velocity and linear acceleration of points that belong to the same body; linear and angular momentum of rigid body; Newton-Euler’s dynamics equations; kinetic energy;
  7. Simplified theory of gyroscope;
  8. Mechanics expressed with use of Lagrange’s formalism; constraints and the constraint equations; main principles used in classifications of the constraints; generalized coordinates; virtual displacements and consequences of the virtual work principle; virtual velocities and the virtual power; generalized forces and the generalized equation of dynamics (d’Alembert’s principle); two types of Lagrange’s equations; selected alternative principles of equilibrium.

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