Golf Swing as a Double Pendulum

By: Jeremy and Aaron

Timeline (5-week):

· Week 1: Model and Analyze 2-rod systems to top of backswing (simple model)

· Week 2: Model and Analyze complex 2-rod system (downswing)

· Week 3: Application of Torque and Forces applied in 2-rod system

· Week 4: Calculating the Kinetic and Potential Energy in the system

· Week 5: Solving the 2-rod system using the Lagrangian Method

· Wrap up: Slow motion camera and capturing real life model of 2-rod system

E:\Double Pendulum\model1.jpg

-Backswing (simple Model) -Downswing (complex model) -Further complex evaluation

-Stationary Model (Before Backswing) -Model at top of Backswing

- We will start to model our double pendulum golf swing at the top of the backswing, which is shown in the picture on the right.

- At the beginning of our model there are two pivot points, pivot O and pivot W.

- Pivot O is the pivot point about our left shoulder which is connected to the pivot W by a straight left arm.

- Pivot W is the pivot by the wrists. This is where the golf club is attached to our wrists.

- The Rod A is classified as our left arm which is connected to both pivots O and W.

- The Rod C is the golf club which is connected at pivot W only.

- The angle between A and C is never less than 90⁰ because 90⁰is our maximum wrist pivot when holding onto the golf club.

Comparison of positions from the top and an angle α through the downswing

Diagrams of Forces Applied to the Model

torque and centrifugal models

Forces acting on model during downswing

Moment of Inertia

Definition:

Moment of Inertia (MOI) is defined as the measure of an objects resistance to changes in its rotational rate.

Parallel Axis Theorem:

The moment of inertia of any object about an axis through its center of mass is the minimum moment of inertia for an axis in that direction in space. The moment of inertia about a parallel axis is the center of mass moment plus the moment of inertia of the entire object treated as a point mass at the center of mass.

Moment of Inertia about center of mass: