Session 293
April 8, 2025
Smirnov A. S., Smolnikov B. A. (Peter the Great SPbPU, IPME RAS)
Stability of equilibrium of a double pendulum with elastic joints under the action of a force of constant modulus
The report discusses the stability of the lower equilibrium position of a double mathematical pendulum with elastic joints under the action of a concentrated force of constant modulus. Four variants of the action of this force in a deflected position are considered, and its conservatism or nonconservatism is established for each of them. Based on these conclusions, the stability conditions are identified in terms of two dimensionless parameters of the problem using a static or dynamic approach, respectively. In addition, the effect of dissipative viscous friction forces in the pendulum joints on the stability of equilibrium is investigated in nonconservative cases. The results obtained are presented in graphical form as stability regions on the parameter plane. They are of interest for analytical mechanics and stability theory, and can also find application in engineering.
Smirnov Alexey S.
–
Candidate of Physical and Mathematical Sciences, Assistant Professor at the Higher school of mechanics and control processes (Peter the Great St. Petersburg Polytechnic University), Junior Researcher at the Laboratory of Mechatronics (Institute of Problems of Mechanical Engineering of the Russian Academy of Sciences). Research interests: analytical mechanics, theory of mechanical oscillations, rigid body dynamics, stability of equilibrium and motion, control of mechanical systems, optimization in mechanics.
Smolnikov Boris A.
–
Candidate of Physical and Mathematical Sciences, Associate Professor at the Higher school of mechanics and control processes (Peter the Great St. Petersburg Polytechnic University), Senior Researcher at the Laboratory of Mechatronics (Institute of Problems of Mechanical Engineering of the Russian Academy of Sciences). Research interests: general mechanics, biomechanics and robotics, rigid body dynamics, motion stability theory, movement of space objects, control theory, evolutionary dynamics.
