holonomic or nonholonomic constraint

Question

Consider the Lagrangian $L(x, y, z, \dot{x}, \dot{y}, \dot{z}) = 1/2 m ( \dot{x}^ 2 + \dot{y}^2 + \dot{z}^2 )− mgz$ with the constraints $y\dot{x} − x\dot{y} = 0.$ How can I prove that these constraints holonomic or nonholonomic?

Answer 1

Taken $\frac{1}{xy}\left(y\dot x-x \dot y\right) = \frac{\dot x}{x}-\frac{\dot y}{y} = 0$ we observe that this comes from $\frac{d}{dt}\left(\ln x-\ln y\right)$ then it is an integrable constraint over the positional variables $x,y$ thus it is a holonomic constraint $\ln x-\ln y=C$ See also here