分析力学一.pptVIP

Analytical Mechanics: Introduction Mechanism of Confinement Mechanism of Confinement Analytical Mechanics Department of Physics Shanghai Jiaotong University 2003 Introduction Newtonian Mechanics By Galileo and Newton Mathematical Principles of Natural Philosophy (1687). Three Laws of Mechanics Analytical Mechanics d’Alembert, Euler, Lagrange, Hamilton Analytical Mechanics by Lagrange (1788) extend to non-mechanical systems. Difference between Newtonian Mechanics and Analytical Mechanics Newtonian: Particles system Force Constraints Analytical: Mechanics system Energy (generalized coordinates) Need not to consider constraints Limitation vc c=2.997925×108m/s speed of light Relative theory h h=6.626×10-34J s Planck constant E×t ~ h or small size Quantum theory Reference 郎道，《力学》 Goldstein， Classical Mechanics 周衍柏，《理论力学》 吴大猷，《古典动力学》 Chapter One Newtonian Mechanics Newton’s Law of Motion First Law (Law of inertia) A body will persevere its state of rest or its state of uniform motion in a straight line unless acted upon by some external force. Second Law Third Law Galileo’s principle of relativity Any mechanical experiments inside a system can not determine whether the system is of rest or of uniform motion in a straight line Newton’s Law is tenable for any inertial reference system Galilean transformation Inertial frame S’ move with velocity v relative to inertial frame S Time t is absolute and concerns nothing with the objects and space. 哲学推理规则 除去那些真实的而又足以说明自然界事物的表象的原因之外，我们承认自然界事物没有更多的原因（简单性） 所以，对于同样的自然界的结果，我们必须尽可能地归之于同样的原因 （因果性） 事物的属性，即不允许增强也不允许削弱，凡是在我们的实验所能到达的范围内发现属于一切物体的属性，都应该视为一切物体的普遍属性 （统一性） 在实验哲学上，我们把用一般归纳法从现象推导的命题，看作准确的或很接近于真实的，虽然可以想象出任何相反的假设，但是直到其他现象出现而使其变得更准确或出现例外之前，仍应如此看待 （真理性） 工欲善其事必先利其器 Expressions of Newton’s Law using different coordinate systems Rectangular coordinate system Polar coordinate system Second Law in Polar coordinate system Spherical Coordinate System Second Law Cylindrical Coordinate System Second Law Intrinsi