- #1
taalf
- 1
- 0
Hi All,
Everyone knows so called "fictitious" forces, also known as "inertial" forces. They are forces felt by some mass point placed in a non-inertial frame. For example: a ball in a moving car or in a carousel.
Maybe most intuitive fictitious forces are centrifugal forces, but there are also Euler forces and Coriolis forces. Formulas for such forces are well known (bold means "vector"):
Euler force: FE = -m ⋅ dΩ/dt × OP
Centrifugal force: FCe = -m ⋅ Ω × (Ω × OP)
Coriolis force: FCo = -m ⋅ 2Ω × V
with:
m the mass of the point,
Ω the rotation vector of the non inertial frame,
OP the position of the point in the non inertial frame,
V the velocity of the point in the non inertial frame.
Know, consider the object is not a mass point, but some solid with a given inertia tensor:
___|Ixx Ixy Ixz|
I = |Iyx Iyy Iyz|
___|Izx Izy Izz|
This solid, put in a non inertial frame, should not only feel fictitious forces, but also fictitious moments.
The question is: how to formulate them?
Everyone knows so called "fictitious" forces, also known as "inertial" forces. They are forces felt by some mass point placed in a non-inertial frame. For example: a ball in a moving car or in a carousel.
Maybe most intuitive fictitious forces are centrifugal forces, but there are also Euler forces and Coriolis forces. Formulas for such forces are well known (bold means "vector"):
Euler force: FE = -m ⋅ dΩ/dt × OP
Centrifugal force: FCe = -m ⋅ Ω × (Ω × OP)
Coriolis force: FCo = -m ⋅ 2Ω × V
with:
m the mass of the point,
Ω the rotation vector of the non inertial frame,
OP the position of the point in the non inertial frame,
V the velocity of the point in the non inertial frame.
Know, consider the object is not a mass point, but some solid with a given inertia tensor:
___|Ixx Ixy Ixz|
I = |Iyx Iyy Iyz|
___|Izx Izy Izz|
This solid, put in a non inertial frame, should not only feel fictitious forces, but also fictitious moments.
The question is: how to formulate them?