title: ÐÐ¸Ð½Ð°Ð¼Ð¸ÐºÐ° Ð¸ ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÑ Ð´Ð²Ð¸Ð¶ÐµÐ½Ð¸Ñ ÑÑÐ³Ð°ÑÐ° Ñ Ð¿ÑÐ¸ÑÐµÐ¿Ð°Ð¼Ð¸
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Dynamics and stability of the movement of the tractor with trailers
Creators: name: ÐÑÑÐ°Ð²ÑÐµÐ², ÐÐ»ÐµÐºÑÐ°Ð½Ð´Ñ
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2019
Subjects: ÑÑÐ³Ð°Ñ Ñ Ð¿ÑÐ¸ÑÐµÐ¿Ð¾Ð¼
ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ Ð´Ð²Ð¸Ð¶ÐµÐ½Ð¸Ñ
ÑÑÐ»Ð¾Ð²Ð¸Ñ ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸
Ð¿ÐµÑÐµÑ Ð¾Ð´Ð½ÑÐµ Ð¿ÑÐ¾ÑÐµÑÑÑ
Ð´Ð¸Ð°Ð³ÑÐ°Ð¼Ð¼Ð° ÐÑÑÐ½ÐµÐ³ÑÐ°Ð´ÑÐºÐ¾Ð³Ð¾
Ð²ÑÐ·ÐºÐ¾Ðµ ÑÑÐµÐ½Ð¸Ðµ
ÑÑÐ³Ð°Ñ Ñ Ð´Ð²ÑÐ¼Ñ Ð¿ÑÐ¸ÑÐµÐ¿Ð°Ð¼Ð¸
tractor with trailer
equations of motion
stability conditions
transients
Vyshnegradsky diagram
viscous friction
tractor with two trailers

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description: Sometimes it happens that a trailer, rolling behind a uniformly moving car on a perfectly smooth horizontal road, loses stability and begins to make dangerous transverse vibrations.
Due to the relevance of this problem, the main purpose of this article is to determine the stability of the movement of a car with a trailer, which as a model is viewed as a uniformly and straightforward moving tractor with a uniaxial trailer. The trailer is connected to the hinge. It is worth emphasizing that the main feature of the system under consideration is the presence of a nonholonomic connection.
Various modifications of the tractor with the trailer are considered.
Consideration begins with a simple model that has one degree of freedom. The angle of deviation of the trailer axis from the direction of movement is chosen as such a degree of freedom. The equation of motion for this model is derived for large and, through linearization of the equation of motion, for small angles of deflection.
Further, a more complex model is considered, taking into account the lateral displacement of the attachment point of the trailer to the towing vehicle - as a result, a new degree of freedom arises. The most detailed study is carried out specifically for this model: it is not only the derivation of the equation of motion and the stability condition, but also the nature of the transition process is established depending on the system parameters. The forms of trailer movement for aperiodic, monotonous and oscillatory transients were obtained. The equation of motion of the system is derived in two ways: using Newton's laws and using the Appel equation. In the course of comparing the equations obtained in two ways, we come to the fact that they completely coincide. In addition, for this model, the effect of viscous friction on the stability region is investigated.
Then a model is considered in which the tractor and trailer are not connected directly, but with the help of a rod (pivotally). During the review, the condition of stability is derived.
In conclusion, a model of a tractor with two trailers is considered and the equation of motion of the second trailer is derived for small deviations.