Heilige Schrift Mech 2 Vo: Mechanik Formeln und Theorien

Heilige Schrift Mech 2 Vo
Lorenz Henfling, 19. März 2026
Zeitfreies Integrieren:
Z xmax
Z ẋmax
ẍdx =
ẋdẋ
xmin
ẋmin
Relativkinematik:
q̇ =
vrel =
df rrel
dt
df q
+ wq × q
dt
va = vf + vrel
vf = vof + wf × rrel
vof =
df rof
+ wf × rof
dt
a = af + arel + ac
af =
df vof
+ wf × vof + w˙f × rrel + wf × wf × rrel
dt
df vrel
arel =
dt
ac = 2(wf × vrel )
SPS:
X
m∗a=
F
Drallsatz:
Ls = w ∗ Is
Lo = Ls + rso × mvso
X
d Lo
+ wf × Lo + rso × (mao ) =
M
dt
f
Träheitstensoren(drehung immer um x):
Dünner Stab

0
0
0
0

0
0 
ml2
12
ml2
12
0
Dünne Scheibe
 mr2
2
0

0
0 
 0
mr 2
4
0
0
mr
4
mr2
 0
0
0

0
0 
Kreisring

mr
2
0
1
2
mr 2
2
Zylinder

mr 2
2
0
mr 2
ml2
4 + 12
0

 0
0

0

0

2
mr
ml
+
4
12
Quader
 m(a2 +b2 )
0
12


m(a2 +l2 )
12
0
0
0
0
0
m(b2 +l2 )
12



Energiemethoden
dT
=P
dt
1
1
T = vs2 m + w2 Is
2
2
T1 + V1 = T2 + V2 + W12
P = Fv + Mw
V = mhg
Linearisierung:
sin(α + β) = sin(α) cos(β) + cos(α) sin(β)
sin(α − β) = sin(α) cos(β) − cos(α) sin(β)
cos(α + β) = cos(α) cos(β) + sin(α) sin(β)
cos(α − β) = cos(α) cos(β) − sin(α) sin(β)
sin(α) → α
cos(α) → 1
tan(α) → α
Schwingungen:
T =
2π
w
ẍ + 2Dwo ẋ + wo2 x = f (t)
Homogene Lösung:
x(t) = xh (t) + xp (t)
D > 1 → xh (t) = C1 eλ1 t + C2 eλ2 t
D = 1 → xh (t) = (C1 + C2 )e−wo t
D < 1 → xh (t) = e−αt (c1 cos(wt) + c2 sin(wt))
p
w = wo 1 − D2 α = Dw0
Partikuläre Lösung
xp = cp1 cos(νt) + cp2 sin(νt)
Stoß:
p′ − p =
X
v2′ − v1′ = −e(v2 − v1 )
X
S L′ − L =
r×S
2