Dynamics Northern Illinos University：动力学北伊利诺斯大学

1、dynamicskinematic vectorskinematic quantities refer to the motion only.positionvelocityaccelerationkinematic vectors of velocity and acceleration are coplanar.dtdxxviii dtrdrvrva iiixva x22r1r1v2v1a2ax1force and masstwo particles can influence each other.masses related to accelerationsmaaaavmbbabvab

2、baaammvmpfpforces on one particlethere is a net force on each particle in an object.this corresponds to the particles acceleration.2222)(dtrmddtrdmamfmrforces on a systemfor n particles in a system the forces add.particles of constant massnntotaldtrmdff1221)(mr)(intf)(extfnnintnexttotaldtrmdfff1221)

3、(1)()(0)(intfnnnetrmmdtdmdtrmdmmf1221221)(nmm1center of massthe weighted average of the positions of the particles is the .the system acts like a single particle.mcmrnetfmrmdtdmfnnet122mrmrncm1cmcmcmnetpvmdtddtrdmdtdfsliding inclined plane1fthe block and inclined plane are both free to move.two fric

4、tionless surfacesmqgmfbg)(qcosmgqsinmgim1)()(ffaambgqqsincosmgmamaqqcos0sin1mgfmamotion of plane2fthe inclined plane has two forces from constraints.upward from tablereaction from blockthe system of linear equations are solved for the accelerations.mqgmfpg)(im12)(fffambgqsin1fmaqcos012ffmg1fqqcossin1mgfmaqqsincosmgmamammgaqqq2sincossinmmgaqqq22sincos1sinnewtonian mechanicsthe result compares to the simple problem of a fixed plane.there were four unknowns in the problem.two accelerationstwo forces of constraintthe constra