# Mathematical model of non-deformed cargo landing system with dampers to rigid plane landing process

DOI: 10.34759/trd-2022-124-12

### Аuthors

Averyanov I. O.1*, Zinin A. V.2**

1. Moscow design industrial complex "MKPK "Universal", 79A, Altufevskoe shosse, Moscow, 127410, Russia
2. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: i.averyanov@mail.ru
**e-mail: allzin@yandex.ru

### Abstract

To calculate dependability measures for developed dropped cargo landing systems with dampers we usually use statistics from similar models and mathematical statistical modelling of landing process. In this article we describe the mathematical model of dynamics landing process for cargo dropped systems with dampers we developed for its further using in statistical modelling.

This mathematical model considers all the phases of dynamic landing process — from the phase when air dampers start resisting to the phase of system stopping — and is able to indicate typical failures like excessive acceleration and system overturn. It should also be appropriate from time cost point of view.

Analysis of sources shows that existing models are not appropriate for the considered task: almost all of them consider only the dampers resisting phase; in case of finite-element models solutions it is not appropriate according to the time cost.

A rigid body with dampers dropped to the rigid landing area (plane) is consided. The body is freely located in 3D space in the beginning of the process as well as the plane. We use dynamic equations of forces and moments equilibrium in 3D space with reactions from dampers and the plane. The body and the plane interaction realizes with contact algorithm. To solve the equations numerical simulation with finite-difference schemes is used.

There are two tasks presented to demonstrate how the developed model works. The first task considers the translational motion of the dropped body with dampers. The second one — complex body movement. As the considered equation system is closed the algorithm we developed has benefits related to the existing solutions from the point of view of time cost. Thus, the dynamic landing model we developed is appropriate for statistical modelling tasks.

### Keywords:

soft landing system, air damper, dropped cargo landing, dependability model of landing process, statistics modelling tasks

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