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Data Definitions

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

RefnameDD:positionIX
Labelx-component of initial position
Symbolpxi
Unitsm
Equationpxi=Lrodsin(θi)
Description
  • pxi is the x-component of initial position (m)
  • Lrod is the length of the rod (m)
  • θi is the initial pendulum angle (rad)
Notes
  • pxi is the horizontal position
  • pxi is shown in Fig:sglpend.
Source
RefBy
RefnameDD:positionIY
Labely-component of initial position
Symbolpyi
Unitsm
Equationpyi=Lrodcos(θi)
Description
  • pyi is the y-component of initial position (m)
  • Lrod is the length of the rod (m)
  • θi is the initial pendulum angle (rad)
Notes
  • pyi is the vertical position
  • pyi is shown in Fig:sglpend.
Source
RefBy
RefnameDD:frequencyDD
LabelFrequency
Symbolf
UnitsHz
Equationf=1T
Description
  • f is the frequency (Hz)
  • T is the period (s)
Notes
  • f is the number of back and forth swings in one second
Source
RefByGD:periodPend, GD:angFrequencyGD, and DD:periodSHMDD
RefnameDD:angFrequencyDD
LabelAngular frequency
SymbolΩ
Unitss
EquationΩ=2πT
Description
  • Ω is the angular frequency (s)
  • π is the ratio of circumference to diameter for any circle (Unitless)
  • T is the period (s)
Notes
Source
RefByGD:periodPend
RefnameDD:periodSHMDD
LabelPeriod
SymbolT
Unitss
EquationT=1f
Description
  • T is the period (s)
  • f is the frequency (Hz)
Notes
Source
RefByGD:periodPend and DD:angFrequencyDD