文档介绍：Introduction to
TATICS
S and
DYNAMICS
Ms
Fs
kˆ
ˆ
ıˆ
F
F1 2
N1 N2
Andy Ruina and Rudra Pratap
Pre-print for Oxford University Press, January 2002
Summary of Mechanics
0) The laws of mechanics apply to any collection of material or ‘body.’ This body could be the overall system of study
or any part of it. In the equations below, the forces and moments are those that show on a free body diagram. Interacting
bodies cause equal and opposite forces and moments on each other.
I) Linear Momentum Balance (LMB)/Force Balance
˙
Equation of Motion F i = L The total force on a body is equal (I)
to its rate of change of linear
momentum.
t
Impulse-momentum 2
F ·dt = impulse is equal to the change in (Ia)
(integrating in time) i
t1 momentum.
˙
Conservation of momentum L = 0 ⇒
When there is force the linear (Ib)
(if F i = 0 ) = −= 0
L L2 L1 momentum does not change.
Statics
˙ F i = 0 If the inertial terms are zero the (Ic)
(if is negligible)
force on system is zero.
II) Angular Momentum Balance (AMB)/Moment Balance
= ˙
Equation of motion MC H C The sum of moments is equal to the (II)
rate of change of angular momentum.
t
Impulse-momentum (angular) 2
M dt = H angular impulse is equal to (IIa)
(integrating in time) C C
t1 the change in angular momentum.
˙
Conservation of angular momentum H = 0 ⇒
C If there is moment about point (IIb)
(if M = 0) = −= 0
C H C H C2 H C1 C then the angular momentum about
point C does not change.
Statics
˙ M = 0 If the inertial terms are zero then the (IIc)
(if is negligible) C
H C total moment on the system is zero.
III) Power Balance (1st law of thermodynamics)
˙+ = ˙+ ˙+ ˙
Equation of motion Q P EK EP Eint Heat flow plus mechanical power (III)
into a system is equal to its change
E˙
in energy (ic + potential +
internal).
t2 t2
fo