Theoretical Models

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

RefnameTM:acceleration
LabelAcceleration
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 (\(\frac{\text{m}}{\text{s}}\))
SourceaccelerationWiki
RefBy
RefnameTM:velocity
LabelVelocity
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 (\({\text{m}}\))
SourcevelocityWiki
RefBy
RefnameTM:NewtonSecLawMot
LabelNewton’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–
RefBy
RefnameTM:NewtonSecLawRotMot
LabelNewton’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–
RefByIM:calOfAngularDisplacement and GD:angFrequencyGD