Rational and Applied Mechanics

1. Front Matter

   Pages i-xviii

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2. Part I KINEMATICS

   1. Front Matter

      Pages 1-1

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   2. Point Kinematics

      • N. N. Polyakhov, M. P. Yushkov, S. A. Zegzhda

      Pages 3-27

   3. Kinematics of the Rigid Solid

      • N. N. Polyakhov, M. P. Yushkov, S. A. Zegzhda

      Pages 29-48

   4. Composite Motion

      • N. N. Polyakhov, M. P. Yushkov, S. A. Zegzhda

      Pages 49-63

3. Part II DYNAMICS. GENERAL ASPECTS OF RATIONAL MECHANICS. FUNDAMENTALS OF ANALYTICAL MECHANICS

   1. Front Matter

      Pages 65-71

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   2. Particle Dynamics

      • N. N. Polyakhov, M. P. Yushkov, S. A. Zegzhda

      Pages 73-141

   3. System Dynamics

      • N. N. Polyakhov, M. P. Yushkov, S. A. Zegzhda

      Pages 143-165

   4. Constrained Motion

      • N. N. Polyakhov, Shervani Khusainovich Soltakhanov, M. P. Yushkov, S. A. Zegzhda

      Pages 167-291

   5. Small Oscillations of Systems

      • P. E. Tovstik, M. P. Yushkov

      Pages 293-326

   6. Dynamics of the Rigid Solid

      • M. P. Yushkov

      Pages 327-377

   7. Variational Principles in Mechanics

      • N. N. Polyakhov, Sh. Kh. Soltakhanov, M. P. Yushkov, S. A. Zegzhda

      Pages 379-429

   8. Statics

      • S. B. Filippov

      Pages 431-463

   9. Integration of Equations in Mechanics

      • N. N. Polyakhov

      Pages 465-496

   10. Elements of the Special Relativity Theory

       • N. N. Polyakhov

       Pages 497-509

4. Back Matter

   Pages 511-520

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Available for the first time in English, this two-volume course on theoretical and applied mechanics has been honed over decades by leading scientists and teachers, and is a primary teaching resource for engineering and maths students at St. Petersburg University.

The course addresses classical branches of theoretical mechanics (Vol. 1), along with a wide range of advanced topics, special problems and applications (Vol. 2). This first volume of the textbook contains the parts “Kinematics” and “Dynamics”. The part “Kinematics” presents in detail the theory of curvilinear coordinates which is actively used in the part “Dynamics”, in particular, in the theory of constrained motion and variational principles in mechanics. For describing the motion of a system of particles, the notion of a Hertz representative point is used, and the notion of a tangent space is applied to investigate the motion of arbitrary mechanical systems. In the final chapters Hamilton-Jacobi theory is applied​ for the integration of equations of motion, and the elements of special relativity theory are presented.

This textbook is aimed at students in mathematics and mechanics and at post-graduates and researchers in analytical mechanics.

• Analytical Mechanics
• Stability of Motion
• Nonlinear Oscillations
• Dynamics and Statics of the Stewart Platform
• Mechanics Under Random Forces
• Elements of Control Theory
• Relations between Nonholonomic Mechanics and the Control Theory
• Vibration and Autobalancing of Rotor Systems
• Physical Theory of Impact
• Statics and Dynamics of a Thin Rod

• Faculty of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg, Russia

  Petr Evgenievich Tovstik

• Faculty of Mathematics and Mechanics, Saint Petersburg State University, St. Petersburg, Russia

  Nikolai Nikolaevich Polyakhov, Mikhail Petrovich Yushkov

• Saint Petersburg State University, St. Petersburg, Russia

  Sergey Andreevich Zegzhda

N. N. Polyakhov (1906-1987), Doctor of Engineering Science,  Professor. Honoured Scientist of the Russian Federation. He graduated from Moscow University, in 1929-1941 worked at Zhukovskii Central Aerohydrodynamic Institute under supervision of academician S.A. Chaplygin, he and V.P. Vetchinkin developed a mathematical model of marine screw propeller. In 1953-1978 he   headed the Chair of Theoretical and Applied Mechanics at the Faculty of Mathematics and Mechanics of Leningrad University. Under his supervision there was written the textbook “Theoretical Mechanics”, which was awarded the First premium of Leningrad University in 1987. N.N. Polyakhov was awarded a number of orders and medals, among them two Orders of Lenin, which was the highest decoration bestowed by the Soviet Union.


M. P. Yushkov, Dr. Sci. in Physics and Mathematics, Professor. He graduated from the Faculty of Mathematics and Mechanics of Leningrad University in 1957 and completed a post-graduate course at the Chair of Theoretical and Applied Mechanics. Since 1960 till now he has been working at this Chair. In 1987 he became a Laureate of the First premium of Leningrad University, and in 2011 he was awarded the Prize of Saint Petersburg State University  “For scientific works”.  He is a co-author (and partially a responsible editor) of four monographs  on nonholonomic mechanics, one of them being translated into Chinese, and another being published in English by Springer Publishing Company. He is awarded a few medals and the Russian Federation Presidential Certificate of Honour and has got the title “Honorary Professor of Saint Petersburg State University”.


S. A. Zegzhda (1935-2015), Dr. Sci. in Physics and Mathematics, Professor. He graduated from the Faculty of Mathematics and Mechanics of Leningrad University in 1958 and completed a post-graduate course at the Chair of Theoretical and Applied Mechanics. Since 1958 till 2015  he had been working at this Chair. In 1987  he became a Laureate of the First premium of Leningrad University, and in 2011 he was awarded the Prize of Saint Petersburg State University  “For scientific works”. He is a co-author of five monographs on the theory of impact and nonholonomic mechanics, one of them being translated into Chinese, and another being published in English by Springer Publishing Company. He was honoured with the title  “Honorary Figure of Russian Higher Education”.


P. E. Tovstik is one of the leading scientists at Saint Petersburg State University (SPbGU). Honoured Scientist of the Russian Federation, recipient of the Order of Honour of the Russian Federation,  Dr. Sci. in Physics and Mathematics.  Since 1978 he has headed the Chair of Theoretical and Applied Mechanics at SPbGU. Of great importance is his contribution to the development and application of asymptotic methods to the theory of thin shells. He is a Laureate of the State Prize of the Russian Federation, a Laureate of M.A. Lavrentiev Prize of the Russian Academy of Sciences, a recipient  of two first premiums of SPbGU for scientific works, an author of 10 books and over 260 papers. Among his pupils there are 9 Drs. Sci. in Physics and Mathematics and over 30 Cands.  Sci. in Physics and Mathematics. 

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