Classical Mechanics
本课程以分析力学为核心，系统讲授拉格朗日力学和哈密顿力学。内容包括约束与广义坐标、变分原理与拉格朗日方程、守恒律与对称性、刚体运动、微振动、哈密顿正则方程、正则变换、泊松括号、哈密顿-雅可比理论等。课程强调从更高的理论视角重新审视经典力学，培养学生的理论物理思维方式，为量子力学、统计力学等后续课程奠定数学和物理基础。
This course focuses on analytical mechanics, systematically teaching Lagrangian mechanics and Hamiltonian mechanics. Topics include constraints and generalized coordinates, variational principles and Lagrange's equations, conservation laws and symmetry, rigid body motion, small oscillations, Hamilton's canonical equations, canonical transformations, Poisson brackets, and Hamilton-Jacobi theory. The course emphasizes re-examining classical mechanics from a higher theoretical perspective, developing students' theoretical physics thinking, and laying the mathematical and physical foundation for subsequent courses such as quantum mechanics and statistical mechanics.
用拉格朗日方法建立双摆系统的运动方程，通过数值模拟研究其非线性动力学和混沌行为。要求实现四阶龙格-库塔算法求解运动方程，绘制不同初始条件下的相空间轨迹。学生需计算李雅普诺夫指数以定量刻画混沌程度，绘制庞加莱截面分析系统的规则与混沌区域，研究系统能量对运动状态的影响，并撰写完整的研究报告。
Establish the equations of motion for a double pendulum system using the Lagrangian method, and study its nonlinear dynamics and chaotic behavior through numerical simulation. Required to implement the fourth-order Runge-Kutta algorithm to solve the equations of motion, plotting phase space trajectories under different initial conditions. Students calculate Lyapunov exponents to quantitatively characterize the degree of chaos, draw Poincaré sections to analyze regular and chaotic regions of the system, study the effect of system energy on motion states, and write a complete research report.