Direct Energy, 2018a

278 12.3 Mechanical Energy Conversion
Energy
storage
device
Generalized
Path
Generalized
Potential
Generalized
Capacity
Constitutive
relationship
Moving
Mass
−→
M
Momentum
in kg·m
s = J·s
m
−→ v Velocity
in m s
m in kg
−→
M = m −→ v
Moving
Mass
−→ v Velocity
in m s
−→
M
Momentum
in kg·m
s = J·s
m
1
m in kg
1
−→ v =
1
−→
M
m
Torsion
Spring
−→ τ torque in
N·m
rad
=
rad
J
Angular
Displacement
−→ θ in
radians
K in
J
rad 2 1
K
Torsion
Spring
Angular
Displacement
−→ θ in
radians
−→ τ torque in
N·m
rad
=
rad
J
in
rad2
J
−→ τ = K
−→ θ
−→ θ =
1
K−→ τ
Energy
Law for
potential
1
m|−→ v | 2 =
2
1
2
| −→ M| 2
m
Conservation
of
Momentum
1
m|−→ v | 2 =
2
1
2
| −→ M| 2
m
Conservation
of
Momentum
1
K|−→ θ | 2 1
= K|−→ θ | 2 =
2
1
K|−→ τ | 2 2
1
K|−→ τ | 2
2 2
Conservation
of Torque
Conservation
of Torque
Table 12.5: Describing more mechanical systems in the language of calculus
of variations.