1 / 9

Moment of Inertia Matrix

Moment of Inertia Matrix. Angular Momentum:. Matrix Equation:. Moment of Inertia Matrix. Solid objects:. Symmetric Matrix:. Matrix has real eigenvalues Matrix has orthogonal eigenvectors Can be rotated into diagonal form. Rotation to Diagonal Form. Eigenvectors for a diagonal matrix:.

kaloni
Download Presentation

Moment of Inertia Matrix

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Moment of Inertia Matrix Angular Momentum: Matrix Equation:

  2. Moment of Inertia Matrix Solid objects: Symmetric Matrix: • Matrix has real eigenvalues • Matrix has orthogonal eigenvectors • Can be rotated into diagonal form

  3. Rotation to Diagonal Form Eigenvectors for a diagonal matrix: Eigenvalues Eigevalue same for all axes Eigenvector depends on axes

  4. Eigenvalues Characteristic equation determines eigenvalues Each eigenvalue Eigenvector

  5. Eigenvectors Are Perpendicular

  6. Rotation to Diagonal Form The matrix that rotates to diagonal form is:

  7. Moment of Inertia for Pyramid Eigenvalues: Eigenvectors:

  8. Diagonalize Matrix? Not diagonal! But we have redundant eigenvalues! That means any linear combination of eigenvectors work equally well.

  9. Parallel Axis Theorem 0

More Related