Mathematical model of a two-link tractor moving on the dirt road

Ground complexes, launching equipment, flying vehicle operation


Moiseev K. A.1*, Panov Y. N.2**, Moiseev K. K.3

1. Peter the Great Strategic Missile Troops Academy, 17, Brigadnaya str., Serpukhov, Moscow region, 142210, Russia
2. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia
3. Gazprom transgaz Moscow, 101, building 1, poselok Gazoprovod, poselenie Sosenskoe, Moscow, 108814, Russia



The article presents a mathematical model of a two-link object movement on the dirt road with periodic unevenness. This model may be useful for the suspension system development at the initial design stages. Mathematical models are presented for different viscoelastic characteristics of the coupling device. It studies the smoothness of the unit in resonant modes of motion of a two-unit tractor. The study of smoothness is based on the intensity curves, which are constructed using the amplitude-frequency characteristics. These characteristics were obtained from the solving the systems of differential equations by analytical matching method or numerical Runge-Kutta method. Matching method is very effective for dynamic systems studying if a differential equation does not exceed the sixth order. It is an organic combination of operator method and the method of variation of constants. Operator method allows construct the equation authorization for the original system of differential equations, and find coefficients of dissipation and frequency of free oscillations of the system under study. As for the method of variation of constants based on the solutions obtained by the operator method, it allows determine a particular solution of the original system of differential equations in the form convenient for analysis.

The obtained results can be applied to ground-car mobile and crawler units, a well as aircraft while studying its landing or emergency landing.

According to the obtained results the authors concluded that the improvement of the smoothness of a two-unit tractor when driving on dirt soil with periodic unevenness requires modification of the viscoelastic characteristics of the hitch mechanism, which, in its turn, alter geometric and weight parameters of the tractor.


two-link caterpillar tractor physical model, two-link caterpillar tractor design scheme, mathematical model, system of differential equations, smoothness of movement, dirt road periodic unevenness, hitch mechanism


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