# Modeling a motion of a non-free system of rigid bodies in the case of calculating damping of the light aircraft landing gear

### Аuthors

Zagidulin A. R.*, Podruzhin E. G.**, Levin V. E.***

Novosibirsk State Technical University, 20, prospect Karla Marksa, Novosibirsk, 630073, Russia

*e-mail: zagidulin@corp.nstu.ru
**e-mail: planer@craft.nstu.ru
***e-mail: levin@craft.nstu.ru

### Abstract

The article describes the mathematical model of the light aircraft landing gear using the method of modeling the motion of a system of rigid bodies with holonomic constraints based on Lagrange equations of the first kind. Traditionally, in design practices for calculating the landing gear damping, Lagrange equations of the second kind are used in generalized coordinates. The disadvantage of this technique is that for each kinematic scheme of landing gear it is necessary to make up its own system of equations, which is a very laborious process. To solve this problem, it is advisable to use a technique based on Lagrange equations of the first kind, which makes it possible to formalize the process of composing equations of motion of a non-free system of rigid bodies. This approach allows us to represent the aircraft landing gear model in the object form – as a set of objects: rigid bodies, power factors and mechanical constraints, which ensures the modularity and extensibility of models.

For the landing gear presented in the article, constraint equations in joints of the construction are written. Expressions are given for the determination of active forces: axial force in the shock absorber, the force of compression of the wheel’s pneumatic. Results of numerical simulation of landing impact are presented in the article.

The method used in calculating damping of the aircraft landing gear differs from methods of calculation previously used, primarily universality. When the system of rigid bodies changes, there is no need to rewrite the equations of motion in generalized coordinates, only the dimensionality of the system changes, and the form of equations is unchanged. Such a universal approach is more algorithmic and simple in numerical implementation.

### Keywords:

aircraft landing, landing gear, liquid-gas shock absorber, Lagrange equations of the first kind, indefinite Lagrange multipliers, system of rigid bodies, holonomic constraints, numerical simulation

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