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1、1(1) the form of action(2)the physical meaning of variables of action(3)the symmetry of action22211( )2ttSmxV x dt( )X ( )x t( ),( )X3Show that the resulting equation of motion is identical to that arising from the more traditional4Show that Lagranges equations for this system are given bywhere5Side

2、 Remark: The functions gab define a metric on the configuration space, and the equations (2) are known as the geodesic equations. They appear naturally in general relativity where they describe a particle moving in curved spacetime. Lagrangians ofthe form (1) also appear in many other areas of physi

3、cs, including the study of solids, the theory of nuclear forces and string theory. In these contexts, the systems are referred to as sigma models.6The motion of an electron of mass m and charge (e) moving in a magnetic field B = A(r) is described by the LagrangianShow that Lagranges equation reproduces the Lorentz force law on the electron7The Lagrangian for a relativistic point particle of mass m is,where c is the speed of light. Derive the equation of motion. Show that it reduces to Newtons equation in the

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