南开大学：《力学》课程教学资源（PPT课件，英文讲稿）Chapter 4 Rigid Body Dynamics

Chapter.4Rigid Body Dynamics

Chapter 4 Rigid Body Dynamics

s 1.Law of conservation of angular momentum1-1 Angular momentumMomentum: Some otherquantity is conservedbeside mechanical energyQ0

Momentum: Some other quantity is conserved beside mechanical energy. §1.Law of conservation of angular momentum 1-1 Angular momentum  0 

History Keplerellipse无法显示该图片无法显示该图片KdsC三dt无法显示dsdrI1FXVXds=二xdr2dt2dt2x=vrsin=by

r v dt dr r dt ds     =  =  2 1 2 1 C dt ds = ds r dr   =  2 1 r v = vrsin = bv   History Kepler ellipse 

Notice:Fysi'sPhysics(2)Rotated90(3)Rotatedaboutdegreesaboutx.x,theny.(1)The book in itsoriginalorientation(4)Rotated90degrees abouty.(5)Rotatedabouty, then x

Notice:

1-2 theorem of angular momentum1. ParticleM=djiM=rxFJ==m政dt2. System of particlesdEJM-4ZM,=-dtM,=M"+M'Mex =rxFexMin =rxFinAdjMerZMin =rx(Fin +F)-E(F+r)xF, =0exdt

1-2 theorem of angular momentum in i ex Mi Mi M    = + dt dj M   = dt d J M i i i i   =   dt dJ Mex   = in i i in Mi r F    =  ex i i ex Mi r F    =  dt dJ M i i   = M r F    =  J r P r vm      =  =     ( + ) −( + ) ij = 0 i j i j in ji in i ij in Mi r F F r r F        2. System of particles 1. Particle