WOLFRAM

Products
  • Wolfram|One
  • Mathematica
  • Wolfram Notebook Assistant + LLM Kit
  • Wolfram|Alpha Notebook Edition
  • System Modeler
  • All Products
Consulting & Solutions
  • Wolfram Consulting
  • Industry Solutions
  • Solutions for Education
Learning & Support
  • Wolfram U Courses
  • Wolfram Language Resources
  • Wolfram Community
  • Support FAQs
  • Contact Support
Company
  • About Wolfram
  • Careers
  • Events
  • Educational Programs
  • All Sites and Resources
Wolfram|Alpha
Wolfram Cloud
Your Account
  • Your Account
  • User Portal
Search

Mechanical Systems  / Function Index  /
Previous section-----Next section

PrincipalAxes
3D

• PrincipalAxes[{Ixx, Iyy, Izz, Ixy, Iyz, Izx}] returns the list {{I1, I2, I3}, {axis1, axis2, axis3}}, where {I1, I2, I3} are the principal moments of inertia and {axis1, axis2, axis3} are the corresponding principal axes of the body represented by the given inertia properties.

• {axis1, axis2, axis3} is actually the rotation matrix from the reference frame in which the inertia properties were specified to the principal axes reference frame.
• See also:
CompositeInertia, GyroFilter, ParallelAxis.

Further Examples

Load the Modeler3D package.

In[1]:=

Here are inertia properties transformed from a noncentroidal to centroidal reference frame.

In[2]:=
Out[2]=

Here are the principal axes of the resulting inertia properties.

In[3]:=
Out[3]=

This rotates the original inertia matrix into the principal frame.

In[4]:=
Out[4]=

Here is the result of combining two sets of inertia properties.

In[5]:=
Out[5]=


  • Products
  • Wolfram|One
  • Mathematica
  • Wolfram|Alpha Notebook Edition
  • Wolfram|Alpha Pro
  • Mobile Apps
  • Finance Platform
  • System Modeler
  • Wolfram Player
  • Wolfram Engine
  • WolframScript
  • Wolfram Workbench
  • Volume & Site Licensing
  • Enterprise Private Cloud
  • Application Server
  • View all...
  • Services
  • Technical Consulting
  • Corporate Consulting
  • For Customers
  • Online Store
  • Product Registration
  • Product Downloads
  • Service Plans Benefits
  • User Portal
  • Your Account
  • Support
  • Support FAQ
  • Customer Service
  • Contact Support
  • Learning
  • Wolfram Language Documentation
  • Wolfram Language Introductory Book
  • Get Started with Wolfram
  • Fast Introduction for Programmers
  • Fast Introduction for Math Students
  • Webinars & Training
  • Wolfram U
  • Summer Programs
  • Videos
  • Books
  • Public Resources
  • Wolfram|Alpha
  • Demonstrations Project
  • Resource System
  • Connected Devices Project
  • Wolfram Data Drop
  • Wolfram + Raspberry Pi
  • Wolfram Science
  • Computer-Based Math
  • MathWorld
  • Hackathons
  • Computational Thinking
  • View all...
  • Company
  • Events
  • About Wolfram
  • Careers
  • Contact
  • Connect
  • Wolfram Community
  • Wolfram Blog
  • Newsletter
© 2025 Wolfram
  • Legal & Privacy Policy
  • Site Map
  • WolframAlpha.com
  • WolframCloud.com