NONLINEAR DYNAMICS OF A FLUID GYROSCOPE

Svetoslav Nikolov; Nataliya Nedkova

Scientific paper ID 1212 : 2015/3

NONLINEAR DYNAMICS OF A FLUID GYROSCOPE

Svetoslav Nikolov, Nataliya Nedkova

The article examines the dynamic behavior of a system of three nonlinear Ordinary Differential Equations describing the behavior of a liquid gyroscope. Our analysis and simulations (with specific choice of parameters) demonstrates that the equilibrium states are three – of saddle and saddle-focus type, and the oscillations are conditionally divided into two levels – "macro" and "micro" level. Changing the parameter leads to modification of the period of the oscillations of the "macro" level.

• Reload article • Open/Download as PDF

нелинейна динамика течен жироскоп качествен и числен анализnonlinear dynamics fluid (liquid) gyroscope qualitative and numerical analysisSvetoslav Nikolov Nataliya Nedkova

BIBLIOGRAPHY

[1] Bardin B., On the orbital stability of pendulum-like motions of a rigid body in the Bobylev-Steklov case, Regular and Chaotic Dynamics, 15(6), 704-716, 2010.

[2] Han Zh., Wang S., Multiple solutions for nonlinear systems with gyroscopic terms, Nonlinear Analysis, 75, 5756-5764, 2012.

[3] Bachvarov S., V. Zlatanov, Ob opredelenii vektora uglovogo uskorenia absolutno tverdova tela, Teoria mehanizmov i mashin, 1(9), pp. 71-80, 2007 (in Russian).

[4] Bachvarov S., V. Zlatanov, Kinematicheskie invarianti i razpredelenie skorostei pri naibolee obshtem dvijenii tverdogo tela, Teoria mehanizmov i mashin, 2(14), pp. 49-60, 2009 (in Russian).

[5] Panchev S. Theory of Chaos. Sofia, Bulgarian Acad. Press, 2001.

[6] Nikolov S., Regular and chaotic behaviour of fluid gyroscope, Comptes rendus de l’Academie bulgare des Sciences, Tome 57, No 1, pp. 19-26, 2004.

[7] Obukhov A., Nileneinie sistemi gidrodinamicheskogo tipa, Nauka, Moskva, 1974.

[8] Obukhov A., Ob integralnih invariantah v sistemah gidrodinamicheskogo tipa, 184(2), pp. 309-312, 1969 (in Russian).

[9] Sonechkin D. Stohastichnost v modeliah obschei circulacii atmosver, Gidrometeozdat, 1984 (in Russian).

[10] Euleri L. Theoria Motus Corporum Solidorum seu Rigidorum. Griefswald, A. F. Rose, 1785, or Euleri L. Opera Omnia Ser. 2 Teubner, 3, 1948 and 4, 1950.

[11] Bautin N, Behavior of dynamical systems near boundary of stability. Nauka, Moscow, 1984 (in Russian).

[12] Matlab, The MathWorks Inc., Natick, MA, 2010.