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This article is cited in 1 scientific paper (total in 1 paper)
Nonlinear physics and mechanics
Qualitative Analysis of the Dynamics of a Trailed
Wheeled Vehicle with Periodic Excitation
E. A. Mikishaninaab a Steklov Mathematical Institute of the Russian Academy of Sciences,
ul. Gubkina 8, 119991 Moscow, Russia
b Chuvash State University,
Moskovskii pr. 15, 428015 Cheboksary, Russia
Abstract:
This article examines the dynamics of the movement of a wheeled vehicle consisting of two
links (trolleys). The trolleys are articulated by a frame. One wheel pair is fixed on each link.
Periodic excitation is created in the system due to the movement of a pair of masses along the
axis of the first trolley. The center of mass of the second link coincides with the geometric center
of the wheelset. The center of mass of the first link can be shifted along the axis relative to the
geometric center of the wheelset. The movement of point masses does not change the center of
mass of the trolley itself. Based on the joint solution of the Lagrange equations of motion with
undetermined multipliers and time derivatives of nonholonomic coupling equations, a reduced
system of differential equations is obtained, which is generally nonautonomous. A qualitative
analysis of the dynamics of the system is carried out in the absence of periodic excitation and
in the presence of periodic excitation. The article proves the boundedness of the solutions of
the system under study, which gives the boundedness of the linear and angular velocities of
the driving link of the articulated wheeled vehicle. Based on the numerical solution of the
equations of motion, graphs of the desired mechanical parameters and the trajectory of motion
are constructed. In the case of an unbiased center of mass, the solutions of the system can be
periodic, quasi-periodic and asymptotic. In the case of a displaced center of mass, the system
has asymptotic dynamics and the mobile transport system goes into rectilinear uniform motion.
Keywords:
trailed wheeled vehicle, nonholonomic problem, qualitative analysis, periodic
excitation, time-dependent dynamic system, stability.
Received: 23.07.2021 Accepted: 01.12.2021
Citation:
E. A. Mikishanina, “Qualitative Analysis of the Dynamics of a Trailed
Wheeled Vehicle with Periodic Excitation”, Rus. J. Nonlin. Dyn., 17:4 (2021), 437–451
Linking options:
https://www.mathnet.ru/eng/nd769 https://www.mathnet.ru/eng/nd/v17/i4/p437
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