Linear and angular momentum conservation for Mass Matrix

[Romik]

Hi all,

I have a question about mass conservation and the way that I should apply it on my problem.

Consider a NxN Mass Matrix, (lets assume 10x10 came from 1D 10 node bar element).
I am going to modify this matrix so I add some different unknowns to all terms (100 terms)

from Physics we know that linear and angular momentum for mass should be conserved, so I have to check these 2 conditions for my modified mass matrix.

how can I do that?

for linear momentum:
is it right if I assume a constant speed V (which is a 10x1 vector) and calculate V^T*M_original*V=V^T*M_modified*V?

what should I do for angular momentum?

I would appreciate if you help me.

Thanks

 

[eljose79]

Hi there,

Great question! Mass conservation is an important principle in physics and it is essential to ensure that it is being properly applied in your problem. In order to check the conservation of linear and angular momentum in your modified mass matrix, you can follow these steps:

1. For linear momentum, your approach of using a constant speed vector V and calculating VT*Moriginal*V=VT*Mmodified*V is a good one. This will allow you to compare the total linear momentum before and after modification and see if it remains the same. However, it is important to note that in this equation, V should be a vector of velocities, not just a constant speed. This will take into account the direction of motion as well.

2. For angular momentum, you can use a similar approach by using a constant angular velocity vector and calculating the total angular momentum before and after modification. However, in this case, you will also need to take into account the position of the mass elements in your matrix. This can be done by using a vector of positions (x,y,z) and calculating the cross product of this vector with the angular velocity vector. Then, you can compare the total angular momentum before and after modification using this equation: VT*(r x V)*Moriginal = VT*(r x V)*Mmodified.

I hope this helps! Let me know if you have any further questions. Good luck with your problem.