# What is an ideal constraint?

1. Oct 11, 2011

### A_B

Hi,

What exactly is the condition for a constraint to be ideal? Let's call the net force of constraint on particle i $\bar{N_i}$. Is the condition
$$\sum_i\bar{N_i}\cdot\delta\bar{r_i}=0?$$
Or is it
$$\bar{N_i}\cdot\delta\bar{r_i}=0$$ for each i? (from which the first follows immediately)

From the second, it follows that all constraint forces must be perpendicular to the allowed virtual displacements, while this does not follow from the first condition.

Also , I don't understand why it is said we can't conclude from
$$\sum_i\bar{K_i}\cdot\delta\bar{r_i}=0$$ (equilibrium for statics)
that the $\bar{K_i}$ are zero BECAUSE the $\bar{r_i}$ are not independent. Suppose they are independent, isn't all we can say that the forces $\bar{K_i}$ would be perpendicular to the virtual displacement?
Is it because
$$\sum_i\bar{K_i}\cdot\delta\bar{r_i}=0$$
must hold for every possible virtual displacement that the $\bar{K_i}$ must be zero?

(i.e. all $\bar{r_i}$ independent -> no constraints -> $\bar{r_i}$ can be in any direction -> $\bar{K_i}$ must be zero)

Thanks

A_B