<?xml version="1.0"?>
<robot xmlns:xacro="http://www.ros.org/wiki/xacro">

  <!-- Specify some standard inertial calculations https://en.wikipedia.org/wiki/List_of_moments_of_inertia -->
  <!-- These make use of xacro's mathematical functionality -->

  <xacro:macro name="inertial_sphere" params="mass radius *origin">
    <inertial>
      <xacro:insert_block name="origin"/>
      <mass value="${mass}" />
      <inertia ixx="${(2/5) * mass * (radius*radius)}" ixy="0.0" ixz="0.0" iyy="${(2/5) * mass * (radius*radius)}" iyz="0.0" izz="${(2/5) * mass * (radius*radius)}" />
    </inertial>
  </xacro:macro>

  <xacro:macro name="inertial_box" params="mass x y z *origin">
    <inertial>
      <xacro:insert_block name="origin"/>
      <mass value="${mass}" />
      <inertia ixx="${(1/12) * mass * (y*y+z*z)}" ixy="0.0" ixz="0.0" iyy="${(1/12) * mass * (x*x+z*z)}" iyz="0.0" izz="${(1/12) * mass * (x*x+y*y)}" />
    </inertial>
  </xacro:macro>

  <xacro:macro name="inertial_cylinder" params="mass length radius *origin">
    <inertial>
      <xacro:insert_block name="origin"/>
      <mass value="${mass}" />
      <inertia ixx="${(1/12) * mass * (3*radius*radius + length*length)}" ixy="0.0" ixz="0.0" iyy="${(1/12) * mass * (3*radius*radius + length*length)}" iyz="0.0" izz="${(1/2) * mass * (radius*radius)}" />
    </inertial>
  </xacro:macro>

</robot>