Dynamic The equations show that, for the whole system, the equilibrium equations given by the dynamic-static method just express the equilibrium between the inertial force system and the external force system, the internal forces are not involved ∑=∑-m=M=-( K m1v)=-x, dt dt ∑g)=2mm)=∑) 21
21 The equations show that, for the whole system, the equilibrium equations given by the dynamic-static method just express the equilibrium between the inertial force system and the external force system, the internal forces are not involved. =− = − = − ( ) = − , dt dK m v dt d Qi mi ai MaC i i 。 dt dL m m v dt d m Q m m a O O ( i ) = − O ( i i ) = − O ( i i ) = −
表明:对整个质点系来说,动静法给出的平衡方程,只 是质点系的惯性力系与其外力的平衡,而与内力无关 ∑=ma=M=4(∑m) ∑)2m( m,\ vo(m -dLo dt 22
22 表明：对整个质点系来说，动静法给出的平衡方程，只 是质点系的惯性力系与其外力的平衡，而与内力无关。 =− =− =− =− dt dK m v dt d Qi mi ai MaC i i ( ) dt dL m m v dt d m Q m m a O O ( i )=− O ( i i )=− O ( i i )=−
Dynamics When you solve dynamical problems of dynamics by the dynamic-static method you have for an arbitrary∑X"+∑Q=0 force system in a plane ∑"+∑Q,=0 ∑m(列)+∑m2)=0。 and you for an arbitrary force system in space ∑X+2.=0,∑m)+∑m)=0 x+∑Q2=0,∑m(F”)+∑mQ)=0 ∑20)+∑g=0,∑mF)+∑m()=0 In practice, we can select the object to e investigate a arbitrarily as in the case al statics. Write dour the equilibrium equations and then solve them 23
23 you have for an arbitrary force system in a plane 。 + = + = + = ( ) ( ) 0 0 , 0 , ( ) ( ) ( ) O i e O i i y e i i x e i m F m Q Y Q X Q and you for an arbitrary force system in space 0 , ( ) ( ) 0。 0 , ( ) ( ) 0, 0 , ( ) ( ) 0, ( ) ( ) ( ) ( ) ( ) ( ) + = + = + = + = + = + = z i e i z z i e i y i e i y y i e i x i e i x x i e i Z Q m F m Q Y Q m F m Q X Q m F m Q In practice, we can select the object to e investigate a arbitrarily as in the case al statics. Write dour the equilibrium equations and then solve them. When you solve dynamical problems of dynamics by the dynamic-static method
力单 用动静法求解动力学问题时, 对平面任意力系: ∑X+∑Qn=0 ∑Y+∑Qn=0 ∑m(F°)+∑m(Q)=0 对于空间任意力系: ∑x+∑Q=0,∑m,(F1)+∑m、Q)=0 ∑Y°+∑Q=0,∑m,(F()+m,(Q)=0 ∑21+∑Q2=0,∑m(F1)+m2(Q)=0 实际应用时,同静力学一样任意选取研究对象,列平衡方 程求解。 24
24 对平面任意力系： + = + = + = ( ) ( ) 0 0 0 ( ) ( ) ( ) O i e O i i y e i i x e i m F m Q Y Q X Q 对于空间任意力系： 0 , ( ) ( ) 0 0 , ( ) ( ) 0 0 , ( ) ( ) 0 ( ) ( ) ( ) ( ) ( ) ( ) + = + = + = + = + = + = z i e i z z i e i y i e i y y i e i x i e i x x i e i Z Q m F m Q Y Q m F m Q X Q m F m Q 实际应用时, 同静力学一样任意选取研究对象, 列平衡方 程求解。 用动静法求解动力学问题时
Dynarnics 815-3 The simplification of a system of inertial forces of a rigid bod The method of simplification is the same as in the case of the theorem of simplification of a force systems in statics. We should treat the virtual inertial force system as an inertial force Ro and an inertial force couple Moo, which are the results of the simplification of the force system to a point O 20=2-ma=-Mac, which is independed on the center of reduction. Moo=>mo(@) which depends on the center of reduction. body is doing, the principle vector of the inertial force system is equal to the product of the weight of the rigid body and the acceleration of the center of mass, the direction is opposite to the direction of the acceleration of the center of mass 25
25 §15-3 The simplification of a system of inertial forces of a rigid body The method of simplification is the same as in the case of the theorem of simplification of a force systems in statics. We should treat the virtual inertial force system as an inertial force and an inertial force couple ,which are the results of the simplification of the force system to a point O: RQ MQO ( ) ,which depends on the center of reduction. , which is independed on the center of reduction. = = = − = − M m Q R Q ma Ma Q O O Q C No matter what motion the rigid body is doing, the principle vector of the inertial force system is equal to the product of the weight of the rigid body and the acceleration of the center of mass, the direction is opposite to the direction of the acceleration of the center of mass