- PII
- 10.31857/S2686740024050017-1
- DOI
- 10.31857/S2686740024050017
- Publication type
- Article
- Status
- Published
- Authors
- Volume/ Edition
- Volume 518 / Issue number 1
- Pages
- 3-9
- Abstract
- A conventional derivation of motion equations in mechanics and field equations in field theory is based on the principle of least action with a proper Lagrangian. With a time-independent Lagrangian, a function of coordinates and velocities that is called energy is constant. This paper presents an alternative approach, namely derivation of a general form of equations of motion that keep the system energy, expressed as a function of generalized coordinates and corresponding velocities, constant. These are Lagrange’s equations with addition of gyroscopic forces. The important fact, that the energy is defined as the function on the tangent bundle of configuration manifold, is used explicitly for the derivation. The Lagrangian is derived from a known energy function. A development of generalized Hamilton’s and Lagrange’s equations without the use of variational principles is proposed. The use of new technique is applied to derivation of some equations.
- Keywords
- Date of publication
- 16.09.2025
- Year of publication
- 2025
- Number of purchasers
- 0
- Views
- 13
References
- 1. Ландау Л.Д., Лифшиц Е.М. Механика. 4-е изд. М.: Наука, 1988.
- 2. Гантмахер Ф.Р. Лекции по аналитической механике. 3-е изд. М.: Физматлит, 2002.
- 3. Зоммерфельд А. Механика. Ижевск: РХД, 2001.
- 4. Ланцош К. Вариационные принципы механики. М.: Мир, 1965.
- 5. José J.V., Saletan E.J. Classical dynamics: a contemporary approach. Cambridge University Press, 1998.
- 6. Винокуров Н.А. Вывод уравнений аналитической механики и теории поля из закона сохранения энергии // УФН. 2014. Т. 184. Вып. 6. С. 641–644.
- 7. Винокуров Н.А. Связь закона сохранения энергии и уравнений движения // УФН. 2015. Т. 185. Вып. 3. С. 335–336.
- 8. Дубровин Б.А., Новиков С.П., Фоменко А.Т. Современная геометрия: Методы и приложения. Т. II. Геометрия и топология многообразий. 4-е изд. М.: Эдиториал УРСС, 1998.
