Sách toán vector/Đồ thị vector

Đồ thị vector

Không gian 1 chiều

Vector đường thẳng ngang

$\overrightarrow{X}=X\overrightarrow{i}$

Vector đường thẳng dọc

$\overrightarrow{Y}=Y\overrightarrow{j}$

Vector đường thẳng nghiêng

$\overrightarrow{Z}=Z\overrightarrow{k}$

Không gian 2 chiều

Vector đường bán kín vòng tròn

$\overrightarrow{R}=R\overrightarrow{r}=\overrightarrow{X}+\overrightarrow{Y}=X\overrightarrow{i}+Y\overrightarrow{j}$

Toán giải tích Vector chuyển động

Vector chuyển động thẳng ngang

$s=\overrightarrow{X}=X\overrightarrow{i}$

$v=\frac{d}{dt}\overrightarrow{X}=\frac{d}{dt}X\overrightarrow{i}=v_x\overrightarrow{i}$

$a=\frac{d^2}{d{t}^2}\overrightarrow{X}=\frac{d^2}{d{t}^2}X\overrightarrow{i}=a_x\overrightarrow{i}$

Vector chuyển động thẳng dọc

$s=\overrightarrow{Y}=Y\overrightarrow{j}$

$v=\frac{d}{dt}\overrightarrow{Y}=\frac{d}{dt}Y\overrightarrow{j}=v_y\overrightarrow{i}$

$a=\frac{d^2}{d{t}^2}\overrightarrow{Y}=\frac{d^2}{d{t}^2}Y\overrightarrow{j}=a_y\overrightarrow{j}$

Vector chuyển động thẳng nghiêng

$s=\overrightarrow{Z}=Z\overrightarrow{k}$

$v=\frac{d}{dt}\overrightarrow{Z}=\frac{d}{dt}Z\overrightarrow{k}=v_z\overrightarrow{k}$

$a=\frac{d^2}{d{t}^2}\overrightarrow{Z}=\frac{d^2}{d{t}^2}Z\overrightarrow{k}=a_k\overrightarrow{k}$

Vector đường bán kín vòng tròn

$s=\overrightarrow{R}=R\overrightarrow{r}$

$v=\frac{d}{dt}(R\overrightarrow{r})=R\frac{d}{dt}\overrightarrow{r}+\overrightarrow{r}\frac{d}{dt}R=R\frac{d}{dt}\overrightarrow{r}=R\omega$

$a=\frac{d^2}{d{t}^2}(R\overrightarrow{r})=R\frac{d^2}{d{t}^2}\overrightarrow{r}+\overrightarrow{r}\frac{d^2}{d{t}^2}R=R\frac{d^2}{d{t}^2}\overrightarrow{r}=R{\omega }^2$

$s=\overrightarrow{R}=\overrightarrow{X}+\overrightarrow{Y}=X\overrightarrow{i}+Y\overrightarrow{j}$

$v=\frac{d}{dt}\overrightarrow{R}=\frac{d}{dt}(\overrightarrow{X}+\overrightarrow{Y})=\frac{d}{dt}(X\overrightarrow{i}+Y\overrightarrow{j})=v_x\overrightarrow{i}+v_y\overrightarrow{j}$

$a=\frac{d^2}{d{t}^2}\overrightarrow{R}=\frac{d^2}{d{t}^2}(\overrightarrow{X}+\overrightarrow{Y})=\frac{d^2}{d{t}^2}(X\overrightarrow{i}+Y\overrightarrow{j})=a_x\overrightarrow{i}+a_y\overrightarrow{j}$

Chuyển Động		s	v	a
Cong		$s(t)$	$\frac{d}{dt}s(t)$	$\frac{d^2}{d{t}^2}s(t)$
Vector đương thẳng ngang	→→	$\overrightarrow{X}=X\overrightarrow{i}$	$\frac{d}{dt}\overrightarrow{X}=\frac{dX}{dt}\overrightarrow{i}=v_x\overrightarrow{i}$	$\frac{d^2}{d{t}^2}\overrightarrow{X}=\frac{d^{2}X}{d{t}^2}\overrightarrow{i}=a_x\overrightarrow{i}$
Vector đương thẳng dọc	↑ ↑	$\overrightarrow{Y}=Y\overrightarrow{j}$	$\frac{d}{dt}\overrightarrow{Y}=\frac{dY}{dt}\overrightarrow{j}=v_y\overrightarrow{j}$	$\frac{d^2}{d{t}^2}\overrightarrow{Y}=\frac{d^{2}Y}{d{t}^2}\overrightarrow{j}=a_y\overrightarrow{j}$
Vector đương thẳng nghiêng		$\overrightarrow{Z}=Z\overrightarrow{k}$	$\frac{d}{dt}\overrightarrow{Z}=\frac{dZ}{dt}\overrightarrow{k}=v_z\overrightarrow{k}$	$\frac{d^2}{d{t}^2}\overrightarrow{Z}=\frac{d^{2}Z}{d{t}^2}\overrightarrow{k}=a_z\overrightarrow{k}$
Vector đương tròn		$\overrightarrow{R}=R\overrightarrow{r}$	$\frac{d}{dt}\overrightarrow{R}$ $R\frac{d}{dt}\overrightarrow{r}+\overrightarrow{r}\frac{d}{dt}R=R\frac{d}{dt}\overrightarrow{r}$	$\frac{d^2}{d{t}^2}\overrightarrow{R}$ $R\frac{d^2}{d{t}^2}\overrightarrow{r}+\overrightarrow{r}\frac{d^2}{d{t}^2}R=R\frac{d^2}{d{t}^2}\overrightarrow{r}$
Vector đương tròn		$\overrightarrow{R}=\overrightarrow{X}+\overrightarrow{Y}$	$\frac{d}{dt}\overrightarrow{R}=\frac{d}{dt}(\overrightarrow{X}+\overrightarrow{Y})$ $\frac{dX}{dt}\overrightarrow{i}+\frac{dY}{dt}\overrightarrow{j}=v_x\overrightarrow{i}+v_y\overrightarrow{j}$	$\frac{d^2}{d{t}^2}\overrightarrow{R}=\frac{d^2}{d{t}^2}(\overrightarrow{X}+\overrightarrow{Y})$ $\frac{d^{2}X}{d{t}^2}\overrightarrow{i}+\frac{d^{2}Y}{d{t}^2}\overrightarrow{j}=a_x\overrightarrow{i}+a_y\overrightarrow{j}$