Theoretical mechanics
1 Theoretical mechanics
理论力学 篇运动学复习
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means 1. Basic contents. I)Kinematics of a Rectilinear motion Uniform velocity uniformly particle Curvilinear motion accelerated, varying velocity Composite motion: absolute motion, relative motion, embroiling motion 2) Kinematics of a Basic motions translation rigid body 3 Plane motion Rotation about a fixed axis Composite motion: composition of rotations about arallel axes 2. Basic equations: pa 1) Motion of a particle Position vector method r=r(0),I>aA dv d2r a- dt dt rectangular coordinates method x=f1( y=f2() 二=f3(
3 1．Basic contents： 1) Kinematics of a particle Rectilinear motion Curvilinear motion Composite motion：absolute motion, relative motion, embroiling motion Uniform velocity. uniformly accelerated , varying velocity 2) Kinematics of a rigid body Basic motions Plane motion Composite motion：composition of rotations about parallel axes translation Rotation about a fixed axis 2．Basic equations: 1) Motion of a particle Position vector method 2 2 ( ) , , dt d r dt dv a dt dr r =r t v = = = rectangular coordinates method ( ) ( ) ( ) 3 2 1 z f t y f t x f t = = = v z v y v x z y x = = = a z a y a x z y x = = =
远动学 基本内容: 直线运动 1,点的运动学曲线运动匀速匀变速变速 合成运动:绝对运动相对运动牵连运动 基本运动{平动 2刚体运动学平面运动定轴转动 合成运动:绕平行轴转动的合成 基本公式 点的运动 dy d2r 矢量法F=(),卩 dt dt2 直角坐标法 x=f1( as y=f2() 二=f3(
4 一．基本内容： 1.点的运动学 直线运动 曲线运动 合成运动：绝对运动,相对运动,牵连运动 匀速,匀变速,变速 2.刚体运动学 基本运动 平面运动 合成运动：绕平行轴转动的合成 平动 定轴转动 二．基本公式 1．点的运动 矢量法 2 2 ( ) , , dt d r dt dv a dt dr r =r t v = = = 直角坐标法 ( ) ( ) ( ) 3 2 1 z f t y f t x f t = = = v z v y v x z y x = = = a z a y a x z y x = = =
emacs =√vx2+v+v Directions are determined by their related cosines a=、a+an2+a natural coordinates method (when trajectory is known) S=f(1),v= dr along the tangential direction Along the tangential direction, anD2 dt dt point to the center of curvature Resultant acceleration; a=var +an, tg(a,n)= Const (uniformly accelerated motion) V=Vo+art SAtyot+a t2 2 (when t=O,V=VO,S=So v2=v02+2ax(-So)
5 2 2 2 x y z v = v + v + v 2 2 2 a = ax + ay + az Directions are determined by their related cosines. natural coordinates method (when trajectory is known) dt ds s = f (t) , v = Along the tangential direction， 2 2 dt d s dt dv a = = Along the tangential direction， 2 v an = point to the center of curvature. Resultant acceleration： n n a a a a a a n = + , tg( , )= 2 2 a = Const. (uniformly accelerated motion): v v a t = 0 + 2 0 0 2 1 s s v t a t = + + 2 ( ) 0 2 0 2 v =v + a s−s (when 0, , ) 0 0 t = v = v s = s