论文标题
非保守动力学系统的古典拉格朗日形式主义
Classical Lagrange formalism for non-conservative dynamical systems
论文作者
论文摘要
经典的拉格朗日形式主义被推广到任意固定（但不一定是保守的）动态系统的情况。结果表明，此类系统的运动方程可以从在系统速度线性的拉格朗日函数的标准方式中得出，没有明确的依赖时间，并且不需要引入任何额外的自由度。我们表明，这种拉格朗日功能的时间对称会导致运动的积分自然概括了能量的概念，但在非保守情况下不与之一致。还讨论了汉密尔顿方程，泊松支架，汉密尔顿 - 雅各比方程，liouville定理和固定行动原则的非保守类似物。例如，我们考虑两个案例，证明了所提出的模式的工作：一维阻尼的谐波振荡器的经典模型和一类特殊的非物理准确可溶解的多维多维动力学模型。
The classical Lagrange formalism is generalized to the case of arbitrary stationary (but not necessarily conservative) dynamical systems. It is shown that the equations of motion for such systems can be derived in the standard ways from the Lagrange functions which are linear in system velocities, have no explicit dependence on time, and do not require the introduction of any additional degrees of freedom. We show that time-symmetry of such Lagrange functions leads to the integrals of motion naturally generalizing the notion of energy but not coinciding with it in non-conservative cases. The non-conservative analogs of Hamilton equations, Poisson brackets, Hamilton-Jacobi equations, Liouville theorem and Principle of Stationary Action are discussed as well. As an example, we consider two cases demonstrating the work of the proposed schema: the classical model of one-dimensional damped harmonic oscillator and a special class of non-physical exactly-solvable multi-dimensional dynamical models.
