I have a 3 degree of freedom system and my equation of motion is like this:(adsbygoogle = window.adsbygoogle || []).push({});

M(q)q_dd + C(q,q_d)q_d+G(q)=0

M(q): inertia matrix

C(q,q_d): Coriolis-centrifugal matrix

G(q): potential matrix.

whereq_dis the first derivative ofqetc andqis a vector of my variables.

q=[θ,γ,a]^{T}

"θ" and "γ" are angles in (rad) and "a" is length in (m).

Now my question is this: I have 3 equations with 3 unknowns but 2 variables are in terms of angles and 1 in terms of distance, so the elements of my inertia matrix don't have the same units. Is that wrong? I mean each equation is consistent in units. The first 2 have units of kg(m/s)^2 while the 3rd has units of kg(m/s^2). I can make the whole thing dimensionless but I read somewhere that the inertia matrix should be symmetric(which it is symmetric at the moment). If I make my equation of motion dimensionless then inertia matrix won't be symmetric anymore. What shall I do?

Any suggestions are welcome

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# Question about Lagrangean dynamics(inertia matrix)

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