According to established tradition, courses on analytical mechanics
include general equations of motion of holonomic and non-holonomic
systems, vari- ational principles, theory of canonical transformations,
canonical equations and theory of their integration (the Hamilton-Jacobi
theorem), integral in- variants, theory of last multiplier and others.
The fundamental laws of mechanics are taken for granted and are not
subject to discussion. The present book is concerned with those issues
of the above listed sub- jects which, in the author's opinion, are most
closely related to engineering problems. Application of the methods of
analytical mechanics to non-trivial prob- lems at the very stage of
constructing the equations requires detailed knowl- edge of the issues
that are normally only briefly touched upon. With this perspective
considerable attention is paid to ways of introducing the gener- alised
coordinates, the theory of finite rotation, methods of calculating the
kinetic energy, the energy of accelerations, the potential energy of
forces of various nature, and the resisting forces. These introductory
chapters, which have to some extent independent significance, are
followed by those on methods of constructing differential equations of
motion for holonomic and non-holonomic systems in various forms. In
these chapters the issues of their interrelations, determination of the
constraint forces and some prob- lems of analytical statics are
discussed as well. It is thought useful to include geometric
considerations of the motion of a material system as motion of the
representative point in Riemannian space.
