Dynamics cheat sheet

11 Formulas
sin 2 x 1cos2x
2
cos 2 x 1cos2x
2
sin 2x 2 sin x cosx
cos2x cos 2 x sin 2 x
1 2 sin 2 x
V p V o r V rel
Velocity of p
relative to o
a p a 0 r r 2 V rel a rel
p
IF rigid body is rotating AND translation at the same time THEN
Take moments around its cg only
ELSE
can also take moments about any other points on it (but
change I)
END IF
o
r
Y
R Y
X
R y
R X
R
x
y
R x
BODY FIXED
COORDINATES
This gives the relation
between the rate of
change with respect to
time of a vector expressed
in a frame of reference
which is body fixed (y,x)
here, to the rate of change
with respect to time of the
same vector expressed
using an inertial frame
coordinates XY.
The omega here is the
angular velocity of the
rigid body rotation, or the
body fixed coordinates,
with respect to the inertial
frame.
d
dt R X,Y d dt R x,y R X,Y
R
r
R r
r
The small disk rotates
at angular speed of
The condition of no slip can
be seen to be
R r r
For the sign of generalized force:
If work done by force takes away
energy from system, then the
sign is negative, else positive. So
Friction will always have negative
sign, so will damping force.
d
dt
cosxt sinxtx t
d
dt
df
dxt
d
dxt
d
cosxt
dt
df
dxt
d
d
cos xt
dxt
d
xt dt
xt dt
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