Ćwiczenia - 16.03.09

(x, y, z)

$$\overrightarrow{r} = x\hat{\text{\ i}} + y\ \hat{j} + z\hat{\text{\ k}}$$

$$d\overrightarrow{r} = dx\hat{\text{\ i}} + dy\ \hat{j} + dz\hat{\text{\ k}}$$

(ρ,φ,θ)

$$\overrightarrow{r} = \rho \bullet \hat{\rho_{0}}$$

$d\overrightarrow{r} = d\ \rho\ \hat{\rho_{0}} +$ $\text{ρ\ d\ θ}\hat{{\ \theta}_{0}} + \rho\operatorname{\ sin}\text{θ\ \ d\ \ φ}\hat{\ \varphi_{0}}$

(r,p,z)

$$\overrightarrow{r} = r\hat{\ r_{0}} + z\ \hat{z_{0}}$$

$$d\overrightarrow{r} = r\ dp\hat{\ p_{a}} + dr\ \hat{r_{0}} + dz\ \hat{z_{a}}$$

(x, y, z)

$$\overrightarrow{V}\ = \dot{\ \overrightarrow{r}}\ = \ \dot{x}\ \hat{\text{i\ }} + \ \dot{y}\ \hat{j}\ + \ \dot{\text{z\ }}\hat{k}$$

(ρ,φ,θ)

$$\overrightarrow{V} = \dot{\overrightarrow{r}} = \dot{\rho}{\hat{\rho}}_{0} + \rho\dot{\theta}\hat{\theta_{0}} + \ \rho\sin{\text{θ\ }\dot{\varphi}\ \hat{\varphi_{0}}\ }$$

(r,p,z)

$\overrightarrow{V} = \dot{\overrightarrow{r}} = r\dot{\rho}{\hat{\rho}}_{0} + \dot{r}\hat{r_{0}} + \ \dot{z}\ \hat{z_{0}}$ prędkość chwilowa

$V\ = \frac{s}{t}$ prędkość średnia