# Translational Inerter

Two-port inertia in mechanical translational systems

Libraries:
Simscape / Foundation Library / Mechanical / Translational Elements

## Description

The Translational Inerter block represents a device that has force proportional to the rate of change of the relative velocity across the ports. It is essentially a two-port inertia that works on the velocity difference between the ports, not the absolute velocity. An inerter is the mechanical equivalent of a capacitor. An inerter with one port connected to ground essentially behaves as a mass with the mass equal to the inerter’s inertance.

Use this block in high performance suspension systems, to decouple weave and roll modes, or in applications where you need to model a passively tuned mass-spring-damper response.

The block is described with the following equations:

`$f=B\frac{dv}{dt}$`
`$v={v}_{R}-{v}_{C}$`

where

• f is force transmitted through the inerter.

• B is inertance.

• v is relative velocity.

• vR and vC are absolute velocities of ports R and C, respectively.

The block positive direction is from port R to port C. This means that the force is positive if it acts in the direction from R to C.

### Variables

To set the priority and initial target values for the block variables prior to simulation, use the Initial Targets section in the block dialog box or Property Inspector. For more information, see Set Priority and Initial Target for Block Variables.

Nominal values provide a way to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. Nominal values can come from different sources, one of which is the Nominal Values section in the block dialog box or Property Inspector. For more information, see Modify Nominal Values for a Block Variable.

## Ports

### Conserving

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Mechanical translational conserving port associated with the rod, that is, the moving body.

Mechanical translational conserving port associated with the case, that is, the stationary body.

## Parameters

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Proportionality coefficient between the force and the rate of change of the relative velocity across the ports.

## Version History

Introduced in R2015b