I think I'm having a really big block over a really small hangup, so forgive me. I'm on an internship and this is my first time working with rotations/change of basis in a real world scenario.(adsbygoogle = window.adsbygoogle || []).push({});

I'm creating a calculator that gives torque in a door mechanism, after a given roll and pitch of the vehicle. It's for the torque in a door check mechanism, but the general torque at the axis of rotation (along door hinges) will suffice for this calculator. I am using rotation matrices to find the component of gravity into and out of the door, then multiplying that against the distance from the axis to the CG to find the torque created by gravity.

I'm setting up the matrices in Excel.

What I've got currently is Rx*Ry*Rz, where Rx is the roll transformation, Ry is the pitch and Rz is the yaw. That successive matrix is then multiplied against the gravity vector. The calculator gives accurate values for the gravity at the center of mass after the pitch and roll, but since I haven't accounted for the distance from the axis to the CG, the Rz matrix has no effect on the gravity.

I feel like I need to add a translation or inertia matrix in there somewhere. The door is being treated as a point mass at the center of gravity.

Rx*Ry*Rz

[1 0 0;0 cos(α) -sin(α);0 sin(α) cos(α)]*[cos(β) 0 sin(β);0 1 0;-sin(β) 0 cos(β)]*[cos(γ) -sin(γ) 0;sin(γ) cos(γ) 0; 0 0 1]

Gravity Vector

[0;0;W]

where α=roll angle, β=pitch angle, γ=yaw angle, W=weight

Thanks SO much with any direction anyone might be able to help with. I've spent hours staring by it at myself, but no one on my team has used linear algebra in decades...

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# Door Rotation Matrix/Change of Basis Plus Translation

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