The Physics:

The physics engine used in these glasses simulates a pendulum. The horizontal and vertical axis forces measured by the LSM303 accelerometer create torque on the virtual pendulum to make it swing. Variables such as friction and gravity can be tweaked to change the responsiveness of the pendulum. The sample code below uses minimal friction and reduced gravity to make the display more lively.

We use the measured acceleration forces to calculate the changes to the momentum of the pendulum. Since the pendulum operates in 2 dimensions, we only look at the horizontal and vertical axis. The 2-dimesional acceleration force vector is converted into a torque based on the rotational position of the pendulum.

And some Math:

OK, now it is time for a little trigonometry:

Since the motion of the pendulum is constrained to circular motion, we need to do a little math with the horizontal and vertical accelerations to calculate the effective torque on the pendulum.

The torque due to horizontal acceleration is proportional to the cosine of the pendulum position in radians.

The torque due to vertical acceleration is proportional to the sine of the pendulum position in radians.

The sum of the two values is the total torque due to acceleration.

After accounting for a little friction, we add the calculated torque to the momentum of the pendulum and calculate a new position & momentum.

The Display:

The pendulum is represented on the Neopixel ring by a cluster of 3-4 pixels with the pixel intensity adjusted proportional to the proximity to the center of the virtual pendulum. This results in a smooth transition and avoids the jumpy appearance of a single pixel. To add some variety, the pixel color changes according to the compass heading calculated from the magnetometer readings of the LSM303.

Alternate Modes of Operation:

The display can switch between normal and “anti-gravity” modes. And between synchronized and mirrored movement of the two eyes. Spin-up and Spin-down effects add visual interest and signal the changes between operating modes.