Selected Recent Publications

• Analytical expressions for stability regions in the Ince–Strutt diagram of Mathieu equation. American Journal of Physics, v. 86 (2018), pp. 257–267. See preprint pdf version.
• Simulation of Space Probes and their Motions Relative to the Host Orbital Station. Computer tools in education, (2018), no. 1, pp. 16–31. See preprint pdf version.
• Oceanic Tides: A Physical Explanation and Modeling. Computer tools in education, (2017), no. 5, pp. 12–34. See preprint pdf version.
• A physically meaningful new approach to parametric excitation and attenuation of oscillations in nonlinear systems. Nonlinear Dynamics, (2017), 88: 2609. doi:10.1007/s11071-017-3398-0. See preprint pdf version (1.33 MB).
• The Envelope of Ballistic Trajectories and Elliptic Orbits. American Journal of Physics, v. 83 (2015), pp. 952–958. See preprint pdf version (1.04 MB).
• Orbital Maneuvers and Space Rendezvous. Advances in Space Research, v. 56 (2015), pp. 2582–2594. See preprint version (pdf, 568 KB).
• Spring pendulum with dry and viscous damping. Communications in Nonlinear Science and Numerical Simulation, v. 20 (2015), pp. 298-315 . See full pdf version (1.88 MB).
• Peculiarities in the energy transfer by waves on strained strings. Physica Scripta, v. 88 (2013) 065402 (7pp). See full pdf version (290 KB).
• Pendulum with a square-wave modulated length. International Journal of Non-Linear Mechanics , v. 55 (2013) 25–34. See abstract and extended pdf version (1.43 MB).
• Oscillations of a simple pendulum with extremely large amplitudes. European Journal of Physics, v. 33 (2012) 1555 – 1563. See full pdf version.
• Misconceptions about the energy of waves in a strained string. Physica Scripta, v. 86 (2012) 035403 (7pp). See full pdf version (210 KB).
• An improved criterion for Kapitza's pendulum stability. Journal of Physics A: Mathematical and Theoretical, v. 44 (2011) 295202 (16 pp). See full pdf version (1.85 MB).
• Comment on 'Energy in one-dimensional linear waves in a string'. European Journal of Physics, v. 32 (2011) L35–L38.
• Extraordinary oscillations of an ordinary forced pendulum. European Journal of Physics, v. 29, No 2 (March 2008) pp. 215 – 233. See abstract and full pdf version (1.56 MB).
• Precession and nutation of a gyroscope. European Journal of Physics, v. 27, No 5 (September 2006) pp. 1071 – 1081. See abstract and full pdf version (270 KB).
• Inertial rotation of a rigid body. European Journal of Physics, v. 27, No 4 (July 2006) pp. 913 – 922. See abstract and full pdf version (270 KB).
• Complicated regular and chaotic motions of the parametrically excited pendulum. Proceedings of IDETC’05 (2005 ASME International Design Engineering Technical Conferences), Long Beach, California, USA, September 24 – 28, 2005. See full pdf version (315 KB).
• Peculiarities of simulations in nonlinear systems. «Computer Simulations – 2005». Proceedings of 6th International Conference, St. Petersburg, June 29 – July 2, 2005. See full pdf version (72 KB).
• Parametric resonance in a linear oscillator at square-wave modulation. European Journal of Physics, v. 26, No 1 (January 2005) pp. 157 – 174. See abstract and full pdf version (588 KB).
• Comment on ‘Eccentricity as a vector’. European Journal of Physics, v. 25, No 4 (2004) pp. L41–L43. See abstract and full pdf version (56 KB).
• Parametric excitation of a linear oscillator. European Journal of Physics, v. 25, No 4 (July 2004) pp. 535 – 554. See abstract and full pdf version (314 KB).
• Square-wave excitation of a linear oscillator. American Journal of Physics, v. 72, No 4 (April 2004) pp. 469 – 476. See abstract and full pdf version (310 KB).
• Families of Keplerian Orbits. European Journal of Physics, v. 24, No 2 (March 2003) pp. 175 – 183. See abstract and full pdf version (160 KB).
• A Dynamical Picture of the Oceanic Tides. American Journal of Physics, v. 70, No 10 (October 2002) pp. 1001 – 1011. See abstract and full pdf version (260 KB).
• Subharmonic Resonances of the Parametrically Driven Pendulum. Journal of Physics A: Mathematical and General, v. 35 (2002) pp. 6209 – 6231. See abstract and full pdf version (404 KB).
• Regular and Chaotic Motions of the Parametrically Forced Pendulum: Theory and Simulations. Computational Science – ICCS 2002, Springer Verlag, LNCS 2331, pp. 1154 – 1169, 2002. See abstract and full pdf version (316 KB).
• On the Dynamic Stabilization of an Inverted Pendulum. American Journal of Physics, v. 69, No 7 (July 2001) pp. 755 – 768. See abstract and full pdf version (260 KB).
• Relative Motion of Orbiting Bodies. American Journal of Physics, v. 69, No 1 (January 2001) pp. 63 – 67. See abstract and full pdf version (171 KB).
• Regular Keplerian Motions in Classical Many-Body Systems. European Journal of Physics, v. 21, No 5 (September 2000) pp. 465 – 482. See abstract and full pdf version (271 KB).
• The Velocity Hodograph for an Arbitrary Keplerian Motion. European Journal of Physics, v. 21, No 4 (July 2000) pp. 297 – 302. See abstract and full pdf version (134 KB).
• Planets and Satellites. Educational software package. Physics Academic Software, American Institute of Physics, 1998. 10th Annual Educational Software Contest winner (1999, Computing in Science and Engineering magazine), European Academic Software Award winner (EASA’2004). See cover, annotation, summary, a journal review (pdf, 564 KB) and manual (pdf, 1.57 MB).
• The Rigid Pendulum – an Antique but Evergreen Physical Model. European Journal of Physics, v. 20, No 6 (November 1999) pp. 429 – 441. See abstract and full pdf version (260 KB).
• Parametric Resonance. Computing in Science and Engineering (CiSE), May – June 1999, pp. 76 – 83. See abstract and full pdf version (163 KB).
• Concise Handbook of Mathematics and Physics. CRC Press (USA), 1997 (528 pp.) See annotation.
• Physics of Oscillations. Educational software package. Physics Academic Software, American Institute of Physics, 1997. European Academic Software Award winner (EASA’96), Ninth Annual Educational Software Contest winner (1998, Computers in Physics magazine). See cover and annotation.

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Computer Simulations (Java applets)

Please note that computer simulations listed below are implemented as Java applets embedded in web pages. Java applets are run on Windows and Mac computers directly in web browsers with Java plugin preinstalled. (Java applets do not run on tablets or pocket devices.) In case Java applets are blocked by your security settings, as a workaround, you can use the Exception Site List feature of your operating system to run. Adding the URL of the blocked application (applet) to the Exception Site List allows the applet to run with some warnings. Unfortunately, this works only in Internet Explorer browser (IE).

• The Oceanic Tides . The educational software program with a detailed User’s Manual for university-level students. It includes simulations that aid understanding various aspects of a difficult but interesting and important subject concerning the origin and properties of the gravitational tide-generating forces. The program illustrates also the properties of stationary tidal waves in the open ocean generated by the sun-induced or moon-induced tidal forces. A simplified model of the ocean (a water shell of equal depth wholly covering the globe) is adopted for the simulation.

  A simplified English version of the Oceanic Tides program (with Java applets representing some of the simulations), and also its Russian version are available directly in the Web. A theoretical background with relevant mathematics for an in-depth study of the subject is included in the detailed User's Manual available as a pdf file (15 pages). The Oceanic Tides program is the winner of 11th Annual Educational Software Contest (2000, IEEE Computer Society, Computing in Science & Engineering magazine).

• Computer Simulations in Classical Dynamics.
  • Collection of Remarkable Three-Body Motions (and also its Russian version). A set of Java applets intended to help students learn and understand the fundamental laws of physics as they apply to the fascinating world of motions of natural and artificial celestial bodies governed by the gravitational forces.
  • Computer illustrations to the laws of motion (and also its Russian version). A set of Java applets which can be useful for college and university students.
  • Inertial rotation of a rigid body (and also its Russian version). The program facilitates understanding of concepts behind rigid body dynamics. Simultaneously with simulating the rigid body motion, the program presents a clear geometrical interpretation of the inertial rotation.
  • Precession and nutation of a gyroscope (and also its Russian version). A small simulation program visualizes the torque-induced motion of a gyroscope and illustrates its principal features to aid understanding about the counterintuitive behaviour of a gyroscope on a qualitative level.

• Physics of Oscillations (and also its Russian version). Lecture demonstrations and a virtual lab for undergraduate students. The simulation programs (Java applets) are executed directly in the browser and allow the user to study natural oscillations, forced oscillations, and parametric oscillations in simple linear and nonlinear mechanical systems. The simulations are based on adequate mathematical models of the investigated physical systems. Each lab work and demonstration includes a User's Manual that gives reference on the theory of the simulated phenomena and suggests activities.

• Pendulum with Square-wave Modulated Length. A virtual lab for undergraduate students. The simulation program (Java applet) is executed directly in the browser and allows the user to study parametric oscillations in a simple familiar nonlinear mechanical system. The lab work includes a detailed user's manual with a relevant theoretical background.

• Torsion Pendulum with Dry and Viscous Friction. A virtual lab for undergraduate students. The simulation program (Java applet) is executed directly in the browser and allows the user to study peculiarities of natural and forced oscillations in a nonlinear system with dry and viscous friction. The lab work includes a paper with a relevant theoretical background.

• Nonlinear Oscillations (the project is under construction). A preliminary version of the simulation software package Nonlinear Oscillations (for MS Windows OS) includes a set of highly interactive programs that visualize the motion of simple nonlinear mechanical oscillatory systems. The project NONLINEAR OSCILLATIONS is not yet finalized: simulations of some other nonlinear systems will be added in the future versions, as well as some new or improved papers with theoretical investigations of the simulated systems. In the package Nonlinear Oscillations the following mechanical systems are simulated:
  • Oscillations and Rotations of a Rigid Pendulum
  • Rigid Pendulum Driven by a Sinusoidal Force
  • Pendulum Driven by a Square-wave Force
  • Pendulum with the Horizontally Driven Pivot
  • Pendulum with the Vertically Driven Pivot
  • Rigid Pendulum with Modulated Length
  • Combined Pendulum with Spring and Gravity
  To install the package on your machine, download the file Nonlinear.zip (7 MB), unzip it and run the standard setup procedure.

  Also a set of Java applets is under development which can be used as undergraduate students virtual on-line lab on nonlinear oscillations. An example of this set is given by the simulation of a simple but important nonlinear system in the lab Free Oscillations and Rotations of a Rigid Pendulum.

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Downloads

• PLANETS AND SATELLITES. The simulation programs of the package are intended to help students learn and understand the fundamental laws of physics as they apply to the charming world of natural and artificial celestial bodies restlessly moving in space. The programs illustrate Kepler's laws, trajectories in velocity space, properties of various families of orbits, evolution of an orbit in the atmosphere, active maneuvers in space and relative motions of orbiting bodies, precession of an orbit, motions of a binary star components, and much more.
  The most fascinating phenomena are revealed in investigating the motions of three or more bodies. Among these are a satellite orbiting a planet that is orbiting a star; a planet in a double-star system; and several planets orbiting a single star. The simulations show how the systems that obey simple physical laws can behave in irregular, chaotic ways. The programs illustrate also possible quite simple motions of celestial bodies described by exact solutions to the three-body problem.
  The software allows the students to construct and investigate a model of the solar system, or to create an imaginary planetary system on their own – complete with the star, planets, moons, comets, asteroids, and satellites, and to explore their orbital motion governed by the gravitational forces. In this wonderful space laboratory we can even reproduce such a possible heavenly catastrophe as a binary encounter of stars which is especially interesting if the stars have planetary systems. For example, the approaching "intruder star" can capture a planet from the system, or even the stars can exchange planets during their rendezvous in space.
  The package PLANETS AND SATELLITES includes a detailed 176-page User’s Manual that gives a theoretical background and suggests students' activities. The manual contains about a hundred of problems. The package of simulation programs PLANETS AND SATELLITES is the 10th Annual Educational Software Contest winner (1999, Computing in Science and Engineering magazine), European Academic Software Award winner (EASA’2004).
  Version 4.0 (2014) is optimized for computers running under MS Windows 7 and Windows 10 operating systems. To install the package on your machine, download the file Planets.zip (7.4 MB), unzip it in a folder on your computer, and run the standard setup procedure (launch the file setup.exe).
  The package PLANETS AND SATELLITES supplements my book Motions of Celestial Bodies: Computer Simulations, IOP Publishing Ltd (2014). The book presents the theoretical background and a detailed description of the simulation programs included in the package.

• PHYSICS OF OSCILLATIONS. The package includes a set of highly interactive programs that allow the user to observe the simulations of simple mechanical oscillatory systems, and obtain time-dependent graphs of the variables that describe the simulated system, phase diagrams and graphs of energy transformations. Graphs and diagrams appear on the screen simultaneously with the display of motion. The suggested experiments have been designed to be plain and obvious. The user can widely modify parameters of the investigated physical systems and conditions of the experiments. The simulations bring to life many abstract concepts related to the physics of oscillations.
  The package PHYSICS OF OSCILLATIONS includes a 160-page User’s Manual that gives a theoretical background for the simulated mechanical systems and suggests students' activities. The manual contains hundreds of problems and exercises. A 95-page Instructor’s Guide gives details of their solutions. The package is the European Academic Software Award winner (EASA’96), Ninth Annual Educational Software Contest winner (1998, Computers in Physics magazine).
  To install the package on your machine (for OS Windows 10), download the file MasterDiskOsc.zip (8.9 MB), unzip it in a folder on your computer, and run the standard setup procedure (launch the file setup.exe). If you are using an earlier Windows version (say, Windows XP or Windows 7), download the file MasterDiskOsc_old.zip (7.3 MB) and launch the file setup.exe.
  The simulations of the package PHYSICS OF OSCILLATIONS serve as illustrations to my book Simulations of Oscillatory Systems, Taylor & Francis Group, CRC Press, USA (2015) (363 pp.). A draft pdf version of the book Simulations of Oscillatory Systems (18 MB) with the theoretical background and a detailed description of the simulation programs can be dowloaded here.

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Contact Information

• E-mail:
• Address: Department of Physics, Saint Petersburg State University
  Uljanovskaya st. 3, Petershoff
  198504 St. Petersburg, Russia
• Web address: http://butikov.faculty.ifmo.ru
• Phone: 8 921 636 8539, Fax: (812) 232 43 18

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Curriculum Vitae

• Graduated from St. Petersburg (former Leningrad) State University in 1962 (Department of Physics). Presently I am full professor of general physics at St. Petersburg State University and St. Petersburg Institute of Fine Mechanics and Optics. I give lecture courses on general physics, optics, quantum theory of solids, theory of oscillations. I have written several textbooks on physics used widely in Russia.
• My research work is associated with solid state physics (quantum theory of electronic paramagnetic resonance, theory of Josephson effects in weak superconductivity), theory of nonlinear oscillations. Several new complicated and even counterintuitive modes of regular and chaotic behavior have been discovered recently in parametrically excited simple nonlinear systems with the help of computer simulations. I have succeeded in finding clear physical explanations for some of these modes, and in a theoretical determination of their boundaries in the parameter space.

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Personal Interests

• During the last years I devote much time and effort to developing (and using in practice) interactive educational software for university-level physics students. My software is a kind of desk-top laboratory in which computer is used as a universal research instrument for investigating models of physical systems rather than simply as a convenient means to search for information and to display it.
• My packages of simulation programs (Physics of Oscillations and Planets and Satellites) with tutorials have been published and distributed by Physics Academic Software, a former project of American Institute of Physics. Presently these packages are available for free directly from this web page (see above).

• My simulation programs are also included in my recently published books Simulations of Oscillatory Systems: with Award-Winning Software, Physics of Oscillations Taylor & Francis Group, CRC Press, USA (2015) ISBN 9781498707688 (363 pp.) and Motions of Celestial Bodies: Computer Simulations. IOP Publishing Ltd (2014) doi:10.1088/978-0-750-31100-7. See Overview.

• With the above mentioned packages of simulation programs, I am trying to change a bit the traditional paradigm of teaching physics at universities. My students do most part of the work on their own, using detailed manuals with assignments, which suggest them certain activity for exploratory usage of the simulation programs. Their work on the assigned projects is a model of a real scientific research.