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:

$$\text{m cdot (a + g cdot sin(theta)) = text{flange\_a.f} + text{flange\_b.f}}$$

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.

This component extends from PartialRigid

Usage

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

Parameters:

Name	Description	Units	Default value
L	Length of component, from left flange to right flange	m	0
m	Mass of the sliding body	kg
g	Acceleration due to gravity; its effect is scaled by sin(theta) using the specified default or user-provided value.	m/s2	-9.80665
theta	Angle defining the path of motion relative to how gravity's influence is calculated as per the component's equations (0 for horizontal).	rad	0

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

Name	Description	Units
s	Absolute position of center of component	m
v	Absolute velocity of the mass along its path of motion	m/s
a	Absolute acceleration of the mass along its path of motion	m/s2

Behavior

$$\begin{array}{rl}\mathtt{flange}\mathtt{\_}\mathtt{a}\mathtt{.}\mathtt{s}\left(t\right)& =-\frac{1}{2}L+s\left(t\right)\\ \mathtt{flange}\mathtt{\_}\mathtt{b}\mathtt{.}\mathtt{s}\left(t\right)& =\frac{1}{2}L+s\left(t\right)\\ v\left(t\right)& =\frac{\mathrm{d}s\left(t\right)}{\mathrm{d}t}\\ a\left(t\right)& =\frac{\mathrm{d}v\left(t\right)}{\mathrm{d}t}\\ (a\left(t\right)+g\sin \left(\mathtt{theta}\right))m& =\mathtt{flange}\mathtt{\_}\mathtt{b}\mathtt{.}\mathtt{f}\left(t\right)+\mathtt{flange}\mathtt{\_}\mathtt{a}\mathtt{.}\mathtt{f}\left(t\right)\end{array}$$

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

$$where `m` is the mass, `a` is its acceleration, `g` is the gravitational acceleration parameter, `\theta` is the angle parameter, and `\text{flange_a.f} + \text{flange_b.f}` represents the sum of external forces applied via the flanges. """ component Mass extends PartialRigid "Mass of the sliding body" parameter m::Dyad.Mass "Absolute velocity of the mass along its path of motion" variable v::Velocity "Absolute acceleration of the mass along its path of motion" variable a::Acceleration "Acceleration due to gravity; its effect is scaled by sin(theta) using the specified default or user-provided value." parameter g::Acceleration = -9.80665 "Angle defining the path of motion relative to how gravity's influence is calculated as per the component's equations (0 for horizontal)." parameter theta::Angle = 0.0 relations "Velocity is the time derivative of absolute position 's' (likely inherited from PartialRigid)" v = der(s) "Acceleration is the time derivative of velocity 'v'" a = der(v) "Newton's second law: relates inertial forces, gravitational effects (per g, theta), and forces from flanges" m * (a + g * sin(theta)) = flange_a.f + flange_b.f metadata {"Dyad": {"icons": {"default": "dyad://TranslationalComponents/Mass.svg"}}} end$$

Flattened 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

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

Test Cases

No test cases defined.

Related

• Examples

• Experiments

• Analyses

• Tests

  • MassDamperSpringFixedTest

  • RelativeSensorsTest

  • SensorsTest