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Data Definitions

This section collects and defines all the data needed to build the instance models.

Velocity

Refname	DD:positionGDD
Label	Velocity
Symbol	$\boldsymbol{v}\text{(}t\text{)}$
Units	$\frac{\text{m}}{\text{s}}$
Equation	$\boldsymbol{v}\text{(}t\text{)}=\frac{\,d\boldsymbol{p}\text{(}t\text{)}}{\,dt}$
Description	$\boldsymbol{v}\text{(}t\text{)}$ is the velocity ( $\frac{\text{m}}{\text{s}}$ ) $t$ is the time ( ${\text{s}}$ ) $\boldsymbol{p}\text{(}t\text{)}$ is the position ( ${\text{m}}$ )
Source	–
RefBy	GD:velocityY2, GD:velocityY1, GD:velocityX2, and GD:velocityX1

Horizontal position of the first object

Refname	DD:positionXDD1
Label	Horizontal position of the first object
Symbol	${p_{\text{x}1}}$
Units	${\text{m}}$
Equation	${p_{\text{x}1}}={L_{1}}\,\sin\left({θ_{1}}\right)$
Description	${p_{\text{x}1}}$ is the horizontal position of the first object ( ${\text{m}}$ ) ${L_{1}}$ is the length of the first rod ( ${\text{m}}$ ) ${θ_{1}}$ is the angle of the first rod ( ${\text{rad}}$ )
Notes	${p_{\text{x}1}}$ is the horizontal position ${p_{\text{x}1}}$ is shown in Fig:dblpend.
Source	–
RefBy	GD:velocityX1

Vertical position of the first object

Refname	DD:positionYDD1
Label	Vertical position of the first object
Symbol	${p_{\text{y}1}}$
Units	${\text{m}}$
Equation	${p_{\text{y}1}}=-{L_{1}}\,\cos\left({θ_{1}}\right)$
Description	${p_{\text{y}1}}$ is the vertical position of the first object ( ${\text{m}}$ ) ${L_{1}}$ is the length of the first rod ( ${\text{m}}$ ) ${θ_{1}}$ is the angle of the first rod ( ${\text{rad}}$ )
Notes	${p_{\text{y}1}}$ is the vertical position ${p_{\text{y}1}}$ is shown in Fig:dblpend.
Source	–
RefBy	GD:velocityY1

Horizontal position of the second object

Refname	DD:positionXDD2
Label	Horizontal position of the second object
Symbol	${p_{\text{x}2}}$
Units	${\text{m}}$
Equation	${p_{\text{x}2}}={p_{\text{x}1}}+{L_{2}}\,\sin\left({θ_{2}}\right)$
Description	${p_{\text{x}2}}$ is the horizontal position of the second object ( ${\text{m}}$ ) ${p_{\text{x}1}}$ is the horizontal position of the first object ( ${\text{m}}$ ) ${L_{2}}$ is the length of the second rod ( ${\text{m}}$ ) ${θ_{2}}$ is the angle of the second rod ( ${\text{rad}}$ )
Notes	${p_{\text{x}2}}$ is the horizontal position ${p_{\text{x}2}}$ is shown in Fig:dblpend.
Source	–
RefBy	GD:velocityX2

Vertical position of the second object

Refname	DD:positionYDD2
Label	Vertical position of the second object
Symbol	${p_{\text{y}2}}$
Units	${\text{m}}$
Equation	${p_{\text{y}2}}={p_{\text{y}1}}-{L_{2}}\,\cos\left({θ_{2}}\right)$
Description	${p_{\text{y}2}}$ is the vertical position of the second object ( ${\text{m}}$ ) ${p_{\text{y}1}}$ is the vertical position of the first object ( ${\text{m}}$ ) ${L_{2}}$ is the length of the second rod ( ${\text{m}}$ ) ${θ_{2}}$ is the angle of the second rod ( ${\text{rad}}$ )
Notes	${p_{\text{y}2}}$ is the vertical position ${p_{\text{y}2}}$ is shown in Fig:dblpend.
Source	–
RefBy	GD:velocityY2

Acceleration

Refname	DD:accelerationGDD
Label	Acceleration
Symbol	$\boldsymbol{a}\text{(}t\text{)}$
Units	$\frac{\text{m}}{\text{s}^{2}}$
Equation	$\boldsymbol{a}\text{(}t\text{)}=\frac{\,d\boldsymbol{v}\text{(}t\text{)}}{\,dt}$
Description	$\boldsymbol{a}\text{(}t\text{)}$ is the acceleration ( $\frac{\text{m}}{\text{s}^{2}}$ ) $t$ is the time ( ${\text{s}}$ ) $\boldsymbol{v}\text{(}t\text{)}$ is the velocity ( $\frac{\text{m}}{\text{s}}$ )
Source	–
RefBy

Force

Refname	DD:forceGDD
Label	Force
Symbol	$\boldsymbol{F}$
Units	${\text{N}}$
Equation	$\boldsymbol{F}=m \boldsymbol{a}\text{(}t\text{)}$
Description	$\boldsymbol{F}$ is the force ( ${\text{N}}$ ) $m$ is the mass ( ${\text{kg}}$ ) $\boldsymbol{a}\text{(}t\text{)}$ is the acceleration ( $\frac{\text{m}}{\text{s}^{2}}$ )
Source	–
RefBy