Spherical Pendulum

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

The top of a pendulum of length hangs from the origin. The mass at the bottom end of the pendulum has coordinates , , , where the vector from the origin to is at an angle θ to the negative axis. The spherical coordinates of are (, , ) with . The Lagrange function and equations give , , and . The integration constants are , , , and the angular momentum . The movement of the spherical pendulum is constrained to the spherical shell between and for all values. The pendulum cannot reach the singular points and for . When the angular momentum vanishes, the pendulum moves in a plane.

Contributed by: Franz Krafft (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

detailSectionParagraph


Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send