The velocity of each node in a spherical mesh is known instantaneously. I would like to characterize the velocity of the whole object knowing that it is allowed to rotate during its motion. How can I proceed for that? Thank you.
Hi,
Basically, you want to know the velocity of the center of gravity of the spherical object, right?
Jean, yes exactly. I thought to compute the mean velocity but it doesn't make sens! I am looking for an efficient and accurate way to characterize the velocity of this rigid spherical body. Thanks!
Well,
Given G the center of gravity of the sphere and A a point on the sphere, the velocity of point A is given from solid mechanics by:
V(A) = V(G) + W x AG (or GA I do not remember exactly)
with W the instantaneous rotation vector of your solid. So I guess, taking a point B such that it is diametrically opposed to A, you can obtained the velocity of the center gravity simply by:
V(A) = V(G) + W x AG
V(B) = V(G) + W x BG = V(G) - W x AG
such that V(A) + V(B) = 2V(G)
This obtained from solid mechanics, so I am not 100% sure you can apply directly to fluid-solid interactions, but may-be it might be worth trying.
Thank you, but your second equation seems to be wrong no? a
I mean the passage from V(G) + W x BG to V(G) - W x AG! How can you do that? a
Ah ok, my bad. So the correct formula should be:
V(A) = V(G) + W x GA
V(B) = V(G) + W x GB = V(G) - W x GA
such that V(A) + V(B) = 2V(G)
No, it wasn't that the problem! The passage V(G) + W x GB = V(G) - W x GA stills to be unjustified! You like to say that W x GB = - W x GA? It is not true! Please remember that you have vectorial quantities here.
Yep. If A and B are diametrically opposed, GB = -GA. That is my point.
Okay, thank you for your answer. I need then to find that point B every time step. Actually my sphere is initially an icosahedron which undergoes several splitting in order to get a finer spherical mesh.
best
a
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