What is the Transformation Rule for the Moment of Inertia Tensor?

AI Thread Summary
The moment of inertia is indeed a tensor, represented as a 3x3 matrix. Its transformation rule aligns with standard tensor transformation principles, despite the coordinates being inside the integrals defining it. The confusion arises from the integration process, but the inertia tensor still adheres to covariant and contravariant transformation rules. Understanding the transformation involves recognizing that the tensor itself is independent of the specific coordinate system used in the integrals. Clarifying this relationship helps in grasping how the moment of inertia tensor behaves under coordinate transformations.
JTC
Messages
100
Reaction score
6
(Forgive me if this is in the wrong spot)

I understand how tensors transform. I can easily type a rule with the differentials of coordinates, say for strain.

I also know that the moment of inertia is a tensor.

But I cannot see how it transforms as does the standard rules of covariant, contravariant, etc.

Because the coordinates are INSIDE the integrals that define the moment of inertia.

yes, I expect it to be a tensor but I cannot see it . Could someone explain?
 
Physics news on Phys.org
Do not worry about the integrands. The inertia tensor is simply a 3x3 matrix and it transforms accordingly.
 

Thread 'Is calling fictitious forces not real just about terminology?'

Hi there, im studying nanoscience at the university in Basel. Today I looked at the topic of intertial and non-inertial reference frames and the existence of fictitious forces. I understand that you call forces real in physics if they appear in interplay. Meaning that a force is real when there is the "actio" partner to the "reactio" partner. If this condition is not satisfied the force is not real. I also understand that if you specifically look at non-inertial reference frames you can...
View full post »

Thread 'Derivation of Hamilton's Principle: Questions'

I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
View full post »

Similar threads

How can I calculate the moment of inertia of any object?
Replies
10
Views
2K
Questions Regarding the Inertia Tensor
Replies
3
Views
2K
How can the moment of inertia of an object be calculated on an arbitrary axis?
Replies
3
Views
1K
I Definition of inertia tensor from a differential geometry viewpoint
Replies
15
Views
2K
Rotational EOM's with non diagonal inertia tensor
Replies
1
Views
2K
Engineering Calculating moment of inertia about z axis
Replies
5
Views
4K
Moment of inertia tensor for two particles
Replies
8
Views
5K
I Axial angular momentum calculation
Replies
12
Views
1K
Why Does the Moment of Inertia Change in Torque-Free Rotation?
Replies
3
Views
2K
I Time derivative of the moment of inertia tensor
Replies
5
Views
3K

Hot Threads

Recent Insights

Back
Top