Holonomic constraints and variables

Let's consider a holonomic constraint:

$$f(q_{1},...,q_{n},t)=0$$

Must every term that compares in the equation be writable as a combination of the variables of a function?

For example, in the holonomic constraint for the pendulum: $$x^{2}+y^{2}-L^{2}=0$$ , i can write $$L$$ as a function of $$x$$ and $$y$$.

Moreover, the math behind this formula wants that every variable $$v\in \left \{ q_{1},...,q_{n},t \right \}$$ must compare in the equation?

• Are you asking if the constraint can be written as a graph of a function? – Qmechanic May 28 at 11:44
• „I can write L as a function of x and y“?. No you can write x as function of L and y, or y as function of L and x – Eli May 28 at 13:35