title: ÐÐ²Ð¸Ð¶ÐµÐ½Ð¸Ðµ ÑÑÐµÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð¼Ð°ÑÑÐ½Ð¸ÐºÐ° ÑÐ¾ ÑÐ»Ð°Ð±Ð¾Ð¹ Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½Ð¾ÑÑÑÑ Ð¿ÑÐ¸ Ð½Ð°Ð»Ð¸ÑÐ¸Ð¸ Ð²Ð½ÐµÑÐ½ÐµÐ³Ð¾ Ð¸Ð»Ð¸ Ð²Ð½ÑÑÑÐµÐ½Ð½ÐµÐ³Ð¾ ÑÑÐµÐ½Ð¸Ñ
title: Motion of a spherical pendulum with weak nonlinearity in the presence of external or internal friction
Creators: name: Ð¡Ð¼Ð¸ÑÐ½Ð¾Ð², ÐÐ»ÐµÐºÑÐ°Ð½Ð´Ñ
name: Ð¡Ð¼Ð¾Ð»ÑÐ½Ð¸ÐºÐ¾Ð², ÐÐ¾ÑÐ¸Ñ
name: "Ð¡Ð¾Ð²ÑÐµÐ¼ÐµÐ½Ð½Ð¾Ðµ Ð¼Ð°ÑÐ¸Ð½Ð¾ÑÑÑÐ¾ÐµÐ½Ð¸Ðµ: Ð½Ð°ÑÐºÐ° Ð¸ Ð¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°Ð½Ð¸Ðµ", Ð¼ÐµÐ¶Ð´ÑÐ½Ð°ÑÐ¾Ð´Ð½Ð°Ñ Ð½Ð°ÑÑÐ½Ð°Ñ ÐºÐ¾Ð½ÑÐµÑÐµÐ½ÑÐ¸Ñ (13; 2024; Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³)
Publisher: name: ÐÐÐÐÐ¢ÐÐ¥-ÐÐ ÐÐ¡Ð¡
Year: 2024
Subjects: ÐÐ°ÑÑÐ½Ð¸ÐºÐ¸
Ð¢ÑÐ¸Ð±Ð¾Ð½Ð¸ÐºÐ°
ÑÐ»Ð°Ð±Ð°Ñ Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½Ð¾ÑÑÑ
Ð²Ð½ÐµÑÐ½ÐµÐµ ÑÑÐµÐ½Ð¸Ðµ
Ð²Ð½ÑÑÑÐµÐ½Ð½ÐµÐµ ÑÑÐµÐ½Ð¸Ðµ
Ð¼ÐµÑÐ¾Ð´ ÑÑÑÐµÐ´Ð½ÐµÐ½Ð¸Ñ
ÑÑÐ°ÐµÐºÑÐ¾ÑÐ¸Ñ Ð´Ð²Ð¸Ð¶ÐµÐ½Ð¸Ñ
weak nonlinearity
external friction
internal friction
averaging method
motion trajectory

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description: The work considers the motion of a spherical pendulum taking into account weak conservative nonlinearity and under the influence of external or internal friction forces. For both friction options, a dissipative function is constructed and equations of motion are derived containing the systemâs own cubic nonlinearity, which are written in a complex form convenient for further actions. Based on the averaging method, an approximate solution is constructed for a system under the action of one or another type of friction, and one can obtain expressions for simpler models from it. The results found are clearly illustrated in the form of trajectories of a spherical pendulum, which correspond to various models, in projection onto the horizontal plane. The solutions obtained make a certain contribution to the theory of motion of a spherical pendulum and can be useful for a variety of practical applications.