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Theoretical Models

This section focuses on the general equations and laws that SglPend is based on.

Acceleration

Refname	TM:acceleration
Label	Acceleration
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	accelerationWiki
RefBy

Velocity

Refname	TM:velocity
Label	Velocity
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	velocityWiki
RefBy

Newton’s second law of motion

Refname	TM:NewtonSecLawMot
Label	Newton’s second law of motion
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 ( $\frac{\text{m}}{\text{s}^{2}}$ )
Notes	The net force $\boldsymbol{F}$ on a body is proportional to the acceleration $\boldsymbol{a}\text{(}t\text{)}$ of the body, where $m$ denotes the mass of the body as the constant of proportionality.
Source	–
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Newton’s second law for rotational motion

Refname	TM:NewtonSecLawRotMot
Label	Newton’s second law for rotational motion
Equation	$\boldsymbol{τ}=\boldsymbol{I}\,α$
Description	$\boldsymbol{τ}$ is the torque ( $\text{N}\text{m}$ ) $\boldsymbol{I}$ is the moment of inertia ( $\text{kg}\text{m}^{2}$ ) $α$ is the angular acceleration ( $\frac{\text{rad}}{\text{s}^{2}}$ )
Notes	The net torque $\boldsymbol{τ}$ on a rigid body is proportional to its angular acceleration $α$ , where $\boldsymbol{I}$ denotes the moment of inertia of the rigid body as the constant of proportionality.
Source	–
RefBy	IM:calOfAngularDisplacement and GD:angFrequencyGD