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Rational and Applied Mechanics

Volume 2. Special Problems and Applications

  • Based on 60 years of experience in teaching theoretical and applied mechanics at Saint Petersburg State University
  • Is unique in the style and depth of presenting the material
  • Corresponds to 4th edition of successful Russian textbook
  • Contains a number of new chapters on both theoretical and applied mechanics

Part of the book series: Foundations of Engineering Mechanics (FOUNDATIONS)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xv
  2. Dynamics. Some Applied Problems of Rational Mechanics

    1. Front Matter

      Pages 1-1
    2. Stability of Motion

      • Petr Evgenievich Tovstik, Mikhail Petrovich Yushkov
      Pages 3-30
    3. Nonlinear Oscillations

      • Petr Evgenievich Tovstik, Mikhail Petrovich Yushkov
      Pages 31-95
    4. Dynamics and Statics of the Stewart Platform

      • Petr Evgenievich Tovstik, Mikhail Petrovich Yushkov, Sergey Andreevich Zegzhda, Tatiana Mikhailovna Tovstik, Tatiana Petrovna Tovstik, V. V. Dodonov
      Pages 97-147
    5. Vibrations and Autobalancing of Rotor Systems

      • Vladimir Grigorévich Bykov, Alexander Svetoslavovich Kovachev, Petr Evgenievich Tovstik
      Pages 149-227
    6. Elements of the Motion Control

      • Petr Evgenievich Tovstik, Natalia Vladimirovna Naumova
      Pages 229-248
    7. Generalized Chebyshev Problem. Nonholonomic Mechanics and Control Theory

      • V. V. Dodonov, Sh. Kh. Soltakhanov, Petr Evgenievich Tovstik, Mikhail Petrovich Yushkov, Sergey Andreevich Zegzhda
      Pages 249-322
    8. Mechanics with Random Forces

      • Petr Evgenievich Tovstik, Tatiana Mikhailovna Tovstik
      Pages 323-351
    9. Physical Impact Theory

      • Sergey Andreevich Zegzhda, Mikhail Petrovich Yushkov
      Pages 353-411
    10. Statics and Dynamics of Thin Rod

      • Alexander Konstantinovich Belyaev, Nikita Fedorovich Morozov, Petr Evgenievich Tovstik, Tatiana Petrovna Tovstik
      Pages 413-435
    11. Flight Dynamics

      • Nikolai Nikolaevich Polyakhov, Mikhail Petrovich Yushkov
      Pages 437-467
  3. Back Matter

    Pages 469-474

About this book

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). Among the special applications addressed in this second volume are: 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.


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



Authors, Editors and Affiliations

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

    Petr Evgenievich Tovstik

  • St. Petersburg, Russia

    Nikolai Nikolaevich Polyakhov

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

    Petr Evgenievich Tovstik, Mikhail Petrovich Yushkov

  • Saint Petersburg State University, St. Petersburg, Russia

    Sergey Andreevich Zegzhda

About the editor

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 Theoreticaland 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. 

Bibliographic Information

  • Book Title: Rational and Applied Mechanics

  • Book Subtitle: Volume 2. Special Problems and Applications

  • Authors: Nikolai Nikolaevich Polyakhov, Petr Evgenievich Tovstik, Mikhail Petrovich Yushkov, Sergey Andreevich Zegzhda

  • Editors: Petr Evgenievich Tovstik

  • Translated by: A. R. Alimov, E. L. Belkind, A. K. Belyaev, A. S. Kovachev, D. A. Lisachenko, V. A. Shelkovina, G. A. Sinilshchikova

  • Series Title: Foundations of Engineering Mechanics

  • DOI: https://doi.org/10.1007/978-3-030-64118-4

  • Publisher: Springer Cham

  • eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)

  • Copyright Information: Springer Nature Switzerland AG 2021

  • Hardcover ISBN: 978-3-030-64117-7Published: 03 December 2021

  • Softcover ISBN: 978-3-030-64120-7Published: 04 December 2022

  • eBook ISBN: 978-3-030-64118-4Published: 02 December 2021

  • Series ISSN: 1612-1384

  • Series E-ISSN: 1860-6237

  • Edition Number: 1

  • Number of Pages: XV, 474

  • Number of Illustrations: 181 b/w illustrations, 6 illustrations in colour

  • Topics: Classical Mechanics, Solid Mechanics, Systems Theory, Control, Control and Systems Theory, Applications of Nonlinear Dynamics and Chaos Theory

Buy it now

Buying options

eBook USD 54.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 69.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 99.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access