Why is mass irrelevant for balanced RW?

[JoMeMi]

Hi there,

I am reading the documentation on REACTIONWHEELSTATEEFFECTOR, and it states that the balanced wheel does not change the mass properties of the spacecraft, because the spin axis and inertia principle axes are aligned with each other as well as the center of mass of the wheel. Why is the mass of the RW irrelevant, because the mass will drastically change the translational dynamics, and the mass of one RW will also affect the moment of inertia for another RW with a different spin axis.

Can someone explain the reasoning behind this? :)

[joaogvcarneiro]

You're right in saying that reaction wheels have mass and, therefore, impact the spacecraft's center of mass and inertia. The idea behind that comment is that a balanced wheel will not introduce any imbalances that come with having an offset between the spin axis and the center of mass of any rigid body, as opposed to imbalanced wheels, which have those cross-coupling contributions.

[JoMeMi]

Hmm, interesting... But when I try printing the total mass of the spacecraft, it is only the mass of the hub, without the mass of the single RW. Will this not completely destroy the results of everything else except the rotation induced by the balanced RW, or is the information about the center of mass and moment of inertia enough? It would not seem so to me.

[joaogvcarneiro]

When you say

printing the total mass of the spacecraft

are you printing the spacecraft.hub.mass property? That will only give you the mass of the hub. If you look into the reaction wheel state effector under the updateEffectorMassProps function, you'll see that we sum all the reaction wheel masses.

[JoMeMi]

I am printing (both before and after executing the simulation) the value of effProps.mEff, which is the value being updated within updateEffectorMassProps, and it returns 0. To try and figure it out, I have also implemented the equations of motion in Matlab, and I can see that to get the same results as Basilisk, the mass of the entire spacecraft must be without the mass of the reaction wheel.

[JoMeMi]

When recording the scMassOutMsg and inspecting the massSC and ISC_PntB_B, I can see that the RW affects neither the total mass or the inertia, and I really can't make this make sense, since if I add a second RW, the presence of the first RW will affect the rotation the second one can induce.

[joaogvcarneiro]

I dug into the code more, and I can explain what you see. A balanced reaction wheel has the following assumptions:

1. The spin axis passes through the center of mass.
2. The spin axis corresponds to one of the wheel's principal axis.

Effectively, this means that the wheel's rotation has no impact on the system's center of mass or the system's inertia. In other words, as the wheel spins, the spacecraft's center of mass and inertia remain constant.

This leads to the way it's implemented in code. Because the spacecraft's center of mass and inertia don't change when the wheel spins, it's assumed that the effector has no mass, center of mass, or inertia contributions. Instead, each wheel's mass, center of mass, and inertia are absorbed into the hub's mass, center of mass, and inertia since the hub's mass properties are always constant. This approach is equivalent to defining the hub's mass properties, not including the wheels, and then summing those contributions per wheel, which I had initially suggested was happening.

While this approach is valid, it can be misleading because it's easy for the user not to embed the wheels' mass properties onto the hub. I'm going to create an issue to address this in the future. It should be a relatively straightforward fix.

As for the cross-coupling between multiple wheels, this is still occurring whether or not their mass properties are embedded into the hub. This effect is implicit through the hub's angular velocity when we project the hub's angular velocity onto the wheel's spin axis.