B Does d'Alembert Principle Hold Without External Forces in a Galactic Frame?

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The discussion centers on the implications of the Lagrange–d'Alembert principle in the context of dark energy and a system of rigid bodies. It questions whether the principle holds true when no external forces act on the system, particularly when the vector summation of all forces relative to a fixed reference frame does not equal zero. The fixed reference frame in question is attached to the center of the Galaxy. This inquiry explores the nuances of equilibrium in the absence of external forces. The implications of these conditions on our understanding of dark energy are significant.
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Hi, I am brainstorming about Dark Energy.

Lagrange–d'Alembert principle is stating that sum of external forces on the system of rigid bodies and sum of system forces must be in quasi static equilibrium.

What if there are no external forces acting on system of bodies and vector summation, relative to fixed reference frame of all m*a in the system of bodies is not equal to zero; would d'Alembert principle still hold?
 
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I have to add; Fixed reference frame is attached to the center of the Galaxy.
 
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