Differentiate time derivative w/ respect to generalized var.

[buildingblocs]

Homework Statement

Solve ∂v/∂θ and ∂v/∂r. (refer to attached image for equations)

Homework Equations

Refer to attached image. note that the velocity is expressed in cylindrical coordinates and attention must be paid to the directional unit vectors e_θ and e_ρ.[/B]

The Attempt at a Solution

Have solution (refer to attached image). However would like to understand the general steps involved such to apply them to other equations with generalised variables and time derivatives.

If any additional information is required to solve please do not hesitate to ask.

 

[robphy]

It looks like you took $\frac{\partial v}{\partial \dot\theta}$ and $\frac{\partial v}{\partial \dot r}$, not $\frac{\partial v}{\partial \theta}$ and $\frac{\partial v}{\partial r}$.

Can you express $\hat e_\rho$ and $\hat e_\theta$ in terms of $\hat x$ and $\hat y$?

 

[buildingblocs]

1)Yes you are correct, I made that mistake.

2)Here are the cylindrical unit vectors expressed in Cartesian unit vectors.

C=Asinθ+Bcosθ
D=Acosθ-Bsinθ

Unit vectors, therefore A=B=1;

C=sinθ+cosθ
D=cosθ-sinθ