Mass

Represents a sliding mass with inertia, subject to external and gravitational forces.

This component models the translational motion of a point mass along a single axis. It considers the mass's inertia, external forces applied through its two mechanical connection flanges (flange_a and flange_b), and a gravitational effect determined by parameters g and theta. The position s, velocity v, and acceleration a are related by v = der(s) and a = der(v). The core dynamic behavior is defined by Newton's second law, expressed as:

\[m \cdot (a + g \cdot \sin(\theta)) = \text{flange_a.f} + \text{flange_b.f}\]

math where m is the mass, a is its acceleration, g is the gravitational acceleration parameter, \theta is the angle parameter, and \text{flange_a.f} + \text{flange_b.f} represents the sum of external forces applied via the flanges.

PartialRigid

Usage

Mass(L=0.0, m, g=-9.80665, theta=0.0)

Parameters:

Connectors

• flange_a - This connector represents a mechanical flange with position and force as the potential and flow variables, respectively. (Flange)
• flange_b - This connector represents a mechanical flange with position and force as the potential and flow variables, respectively. (Flange)

Variables

Behavior

\[ \begin{align} \mathtt{flange\_a.s}\left( t \right) &= - \frac{1}{2} L + s\left( t \right) \\ \mathtt{flange\_b.s}\left( t \right) &= \frac{1}{2} L + s\left( t \right) \\ v\left( t \right) &= \frac{\mathrm{d} s\left( t \right)}{\mathrm{d}t} \\ a\left( t \right) &= \frac{\mathrm{d} v\left( t \right)}{\mathrm{d}t} \\ \left( a\left( t \right) + g \sin\left( \mathtt{theta} \right) \right) m &= \mathtt{flange\_b.f}\left( t \right) + \mathtt{flange\_a.f}\left( t \right) \end{align} \]

Source

# Represents a sliding mass with inertia, subject to external and gravitational forces.
#
# This component models the translational motion of a point mass along a single axis. It considers the mass's inertia, external forces applied through its two mechanical connection flanges (`flange_a` and `flange_b`), and a gravitational effect determined by parameters `g` and `theta`. The position `s`, velocity `v`, and acceleration `a` are related by `v = der(s)` and `a = der(v)`. The core dynamic behavior is defined by Newton's second law, expressed as:
# ```math
# m \cdot (a + g \cdot \sin(\theta)) = \text{flange_a.f} + \text{flange_b.f}
# ```math
# where `m` is the mass, `a` is its acceleration, `g` is the gravitational acceleration parameter, `\theta` is the angle parameter, and `\text{flange_a.f} + \text{flange_b.f}` represents the sum of external forces applied via the flanges.
component Mass
  extends PartialRigid
  # Mass of the sliding body
  parameter m::Dyad.Mass
  # Absolute velocity of the mass along its path of motion
  variable v::Velocity
  # Absolute acceleration of the mass along its path of motion
  variable a::Acceleration
  # Acceleration due to gravity; its effect is scaled by sin(theta) using the specified default or user-provided value.
  parameter g::Acceleration = -9.80665
  # Angle defining the path of motion relative to how gravity's influence is calculated as per the component's equations (0 for horizontal).
  parameter theta::Angle = 0.0
relations
  # Velocity is the time derivative of absolute position 's' (likely inherited from PartialRigid)
  v = der(s)
  # Acceleration is the time derivative of velocity 'v'
  a = der(v)
  # Newton's second law: relates inertial forces, gravitational effects (per g, theta), and forces from flanges
  m*(a+g*sin(theta)) = flange_a.f+flange_b.f
metadata {"Dyad": {"icons": {"default": "dyad://TranslationalComponents/Mass.svg"}}}
end

# Represents a sliding mass with inertia, subject to external and gravitational forces.
#
# This component models the translational motion of a point mass along a single axis. It considers the mass's inertia, external forces applied through its two mechanical connection flanges (`flange_a` and `flange_b`), and a gravitational effect determined by parameters `g` and `theta`. The position `s`, velocity `v`, and acceleration `a` are related by `v = der(s)` and `a = der(v)`. The core dynamic behavior is defined by Newton's second law, expressed as:
# ```math
# m \cdot (a + g \cdot \sin(\theta)) = \text{flange_a.f} + \text{flange_b.f}
# ```math
# where `m` is the mass, `a` is its acceleration, `g` is the gravitational acceleration parameter, `\theta` is the angle parameter, and `\text{flange_a.f} + \text{flange_b.f}` represents the sum of external forces applied via the flanges.
component Mass
  # Left translational 1D flange
  flange_a = Flange() [{"Dyad": {"placement": {"icon": {"x1": -50, "y1": 450, "x2": 50, "y2": 550}}}}]
  # Right translational 1D flange
  flange_b = Flange() [{"Dyad": {"placement": {"icon": {"x1": 950, "y1": 450, "x2": 1050, "y2": 550}}}}]
  # Absolute position of center of component
  variable s::Dyad.Position
  # Length of component, from left flange to right flange
  parameter L::Length = 0.0
  # Mass of the sliding body
  parameter m::Dyad.Mass
  # Absolute velocity of the mass along its path of motion
  variable v::Velocity
  # Absolute acceleration of the mass along its path of motion
  variable a::Acceleration
  # Acceleration due to gravity; its effect is scaled by sin(theta) using the specified default or user-provided value.
  parameter g::Acceleration = -9.80665
  # Angle defining the path of motion relative to how gravity's influence is calculated as per the component's equations (0 for horizontal).
  parameter theta::Angle = 0.0
relations
  flange_a.s = s-L/2
  flange_b.s = s+L/2
  # Velocity is the time derivative of absolute position 's' (likely inherited from PartialRigid)
  v = der(s)
  # Acceleration is the time derivative of velocity 'v'
  a = der(v)
  # Newton's second law: relates inertial forces, gravitational effects (per g, theta), and forces from flanges
  m*(a+g*sin(theta)) = flange_a.f+flange_b.f
metadata {"Dyad": {"icons": {"default": "dyad://TranslationalComponents/Mass.svg"}}}
end

Test Cases

No test cases defined.

Related

• Examples
• Experiments
• Analyses
• Tests
  • MassDamperSpringFixedTest
  • RelativeSensorsTest
  • SensorsTest