Lipiński K., Fundamentals of classical and analytical mechanics
Słowa kluczowe / Key words: theory of vectors, kinematics of particles, dynamics of particles, spherical and general motion of rigid bodies, simplified theory of gyroscope, Lagrange proposed reformulation of mechanics
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:
- Few words of introduction focusing on the domain, branches and the primary assumptions of mechanics;
- A brief introduction to the fundamental concepts and principles of algebra of vectors;
- Kinematics of particles, mainly focused on non-Cartesian coordinates used in mathematical descriptions of kinematics;
- 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;
- 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;
- 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;
- Simplified theory of gyroscope;
- 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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