I'm learning about Lagrange equations and was wondering if the lagrange equations would hold with moving constraints. I've searched a lot on the internet, but never came across my exact question. I know that in order to use lagrange equation the system needs to be holonomic. Although I find the definition of a holonomic system somewhat hard to grasp it goes as follows: If we can write the constraints as follows $$\vec{r}_{a}=\vec{r}_{a}\left(q_{1}, \ldots, q_{K}\right)$$ we are dealing with a holonomic system and if not we're dealing with a non-holonomic system.

Knowing this I would answer on my question that the lagrange equations do not hold, because my interpretation of a moving constraint is that it is time dependent and does not fit the definition of a holonomic system. I like to convince myself of my answer but I'm not quite convinced.

If someone could explain to me why I'm wrong or mayby why my argument is right it would be very helpful!

Thanks in advance

I'm learning about Lagrange equations and was wondering if the lagrange equations would hold with moving constraints. I've searched a lot on the internet, but never came across my exact question. I know that in order to use lagrange equation the system needs to be holonomic. Although I find the definition of a holonomic system somewhat hard to grasp it goes as follows: If we can write the constraints as follows $$\vec{r}_{a}=\vec{r}_{a}\left(q_{1}, \ldots, q_{K}\right)$$ we are dealing with a holonomic system and if not we're dealing with a non-holonomic system.

Knowing this I would answer on my question that the lagrange equations do not hold, because my interpretation of a moving constraint is that it is time dependent and does not fit the definition of a holonomic system. I like to convince myself of my answer but I'm not quite convinced.

If someone could explain to me why I'm wrong or maybe why my argument is right it would be very helpful!