Can someone explain this can't understand notation

[carrotstien]

from wikipedia for
"The most general equation for rotation of a rigid body in three dimensions about an arbitrary origin O with axes x, y, z is"...

i thought that the sum of the torques on a system is just equal to d/dt(L)=d/dt(Iw)...apparently not - but i can't understand the notation like, what is b, G..etc

 

[cronxeh]

This article explains it better:
http://www.statemaster.com/encyclopedia/Rigid-body-dynamics

I is the moment of inertia tensor
ω is the angular velocity (a vector)
ωq is the angular velocity about axis q.
M is the total mass.
bG/O is the vector from O to the body's center of mass.
RO is the position of O.
t is time.
τO,j is one of the N moments about O.

 

[sir-pinski]

Sure, I can try to explain the notation used in the Wikipedia article you mentioned.

Firstly, the equation you mentioned about the sum of torques on a system is correct. However, it is a simplified version and applies to a specific case of a rigid body rotating about a fixed axis. The more general equation for rotation of a rigid body takes into account rotations about an arbitrary origin and axes, and therefore has more variables and notation involved.

Let's break down the equation and notation step by step.

"The most general equation for rotation of a rigid body in three dimensions about an arbitrary origin O with axes x, y, z is":

- "most general equation" means that this equation applies to any type of rotation of a rigid body, not just a specific case.
- "rotation of a rigid body in three dimensions" refers to the movement of a rigid body in three-dimensional space.
- "about an arbitrary origin O" means that the rotation is not limited to a fixed point or axis, but can occur around any point O in space.
- "with axes x, y, z" refers to the three axes (x, y, and z) that define the orientation of the rigid body.

Now, let's look at the actual equation:

L = Iω

- L represents the angular momentum of the rigid body, which is a measure of its rotational motion.
- I represents the moment of inertia of the rigid body, which is a measure of how its mass is distributed around its axis of rotation.
- ω represents the angular velocity of the rigid body, which is the rate of change of its orientation with respect to time.

The equation basically states that the angular momentum of a rigid body is equal to its moment of inertia multiplied by its angular velocity.

Next, let's look at the variables you mentioned: b and G.

- b represents the position vector of the center of mass of the rigid body with respect to the origin O. This vector is used to calculate the moment of inertia.
- G represents the angular momentum of the rigid body with respect to the origin O. This is related to the angular momentum L mentioned earlier, but takes into account the position of the center of mass.

I hope this helps to clarify the notation and equation for you. Keep in mind that this is a complex topic and may require further reading and understanding. Don't hesitate to ask for further clarification if needed.