1.3.3 A spherical pendulum is physically equivalent to a simple pendulum. It consists of a mass...

 

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1.3.3 A spherical pendulum is physically equivalent to a simple pendulum. It consists of a mass m which is attached to one end of a light inextensible cord of length a while the other end of the cord is fixed. The motion is not just confined to a plane, but occurs freely in space. So it is not just the inclination of the cord that moves, but also the orientation of the vertical plane through the cord. Determine the Lagrangian function of the pendulum. a 1.3.4 Write down expressions in generalized coordinates for the Lagrangian functions of the following systems. 1.3.4.1 A particle which is constrained to remain on the surface of a sphere. 1.3.4.2 A particle that is constrained to the surface of a cylinder. 1.3.4.3 A particle that is constrained to remain on the surface of a cone with half-angle a and verter downwards. 1.3.3 A spherical pendulum is physically equivalent to a simple pendulum. It consists of a mass m which is attached to one end of a light inextensible cord of length a while the other end of the cord is fixed. The motion is not just confined to a plane, but occurs freely in space. So it is not just the inclination of the cord that moves, but also the orientation of the vertical plane through the cord. Determine the Lagrangian function of the pendulum. a 1.3.4 Write down expressions in generalized coordinates for the Lagrangian functions of the following systems. 1.3.4.1 A particle which is constrained to remain on the surface of a sphere. 1.3.4.2 A particle that is constrained to the surface of a cylinder. 1.3.4.3 A particle that is constrained to remain on the surface of a cone with half-angle a and verter downwards.