The formula of diagApprox

[YilingQiao]

Hi,

I'm a student and working on physics simulation.

I'm looking for some help with the formula of diagApprox. Specifically, I am curious about the rationale behind its computation as follows:

(invweight + f * f * invweight) * 2 * f * f / m.opt.impratio

Could you please direct me to any papers or other references that explain the meaning behind this formula?

The relevant MuJoCo code is here:

mujoco/src/engine/engine_core_constraint.c

Line 1207 in 5ac5cfb

dA[i+2*j] = dA[i+2*j+1] = tran + fri*fri*(j < 2 ? tran : rot);

Or the equivalent MJX code here:

mujoco/mjx/mujoco/mjx/_src/constraint.py

Line 386 in 5ac5cfb

invweight = invweight * 2 * fri[0] * fri[0] / m.opt.impratio

Thank you so much for your time!