Exploring Ball Physics: Understanding Falling and Bouncing Dynamics in C++

1. LAB 3: BALL PHYSICS CS 282

2. Housekeeping… • Questions about Assignment 1? • Questions about last week’s lab? • Otherwise, please sit next to your partner (or someone else if your partner isn’t here)!

3. What’s the plan for today? • We are going to make a ball fall and bounce off a table… with physics! • In a nutshell, • Get a ball to fall in the framework • Collision checking • Changing velocity • Energy Relationships • And for the over achievers… • Realistic animation

4. Framework • First of all, download the framework for today’s lab ( Resources in class website) • Take a look at the framework. Namely • The body class (body.h and body.cpp) • lab3.cpp (the driver) • Notice that the body class has • 3 vectors: position, velocity, acceleration • 2 scalars: mass, energy • So now let’s make the ball fall!

5. Exercise 1: Falling Ball (Integration) • How do you update the position of the ball? • For now, we are going to assume the ball can only move in the y-direction, so ignore x and z. • If you know the velocity and the delta time, you can update the position! • How do we get delta time? • Since we have a clock class, and a clock called “delta_time” in our driver, all we need to do is call the measure_reset() function • We use measure_reset because delta time should be reset after its value is read.

6. Exercise 1 • Go into body.cpp • Edit the “update_position” function • Add the C++ equivalent of:y_position= y_position+ ( y_velocity* delta_t ) • Go into lab3.cpp • Notice the variable “sphere” and its parameters • For this exercise, we let the sphere have an initial velocity of -2.0 • Look at the DrawGLScene() function • Notice the part commented “Sphere Physics” • Under “Sphere Physics” use the global_time object and update_position function to correctly update sphere’s postion.

7. Success!.... Wait, what?! • Our ball fell magnificently! • But it also fell through the table… • Since we never check for a collision between the ball and the table, there is no interaction between them • We need to fix that!

8. Exercise 2a: Collision Checking • Things to consider when doing collision • The position of your object (in this case, the ball) • It’s size ( radius for us ) • The position of the object we want to check • You want to make the ball stop when it hits the table. • The table is situated at ( 0.0, -0.5, 0.0) • The radius of the ball is 0.5 • Conveniently, this allows us to just check the collision at 0.0 • Go into body.cpp • Modify the update_positionfunction • The ball should stop when it touches the table

9. Exercise 2b: Velocity • Our ball now stops at the table… • But something is still wrong • The ball is falling at constant speed – which would be OK if there was no acceleration. • Unfortunately for us, we have gravity • So we need to update our velocity based on acceleration • Acceleration due to gravity is -9.81 m/s2

10. Exercise 2b: Velocity • Examine the your change toupdate_position • It should be testing for y_position >=0 • Add this same check to update_velocity • Inside the check, add the C++ equivalent of: • y_velocity= y_velocity+ (delta_t * gravity) • This should be the only statement inside of this check right now. • At this point, our ball will accelerate until it touches the table.

11. Great! We have an accelerating, colliding ball now! • But something is still missing…

12. Please switch drivers!

13. Exercise 3: Bouncing • Next we will make the ball bounce. • For now, we will just switch the sign of the y velocity once the ball has hit the ground • Go to body.cpp • In update_velocity, add a check to switch the velocity sign. In other words: • If y_position< 0, switch y_velocitysigns • The ball now bounces up and down!

14. Energy • We are still missing one more thing – when the ball hits the ground, it should not bounce up to the same height. • The ball starts off with a certain amount of potential energy. When it hits the ground, this energy is converted to both kinetic and thermal energy. • Thus we our ball will have a lower kinetic energy, and will not bounce as high!

15. Exercise 4: Implementing Energy • First, you need to figure out the initial potential energy of the ball. • Ep = m*g*h • mass * 9.81 * height of the ball • Go to body.cpp, and calculate energy in the constructor (since we know all our parameters at that point already!) • Next, we need to remove some things • Remove the if statement in update_position • Remove the if-else in update_velocity

16. Exercise 4 • At this point, your update_velocity and update_position functions should have 1 line of code. • We need to know, however, when the ball has hit the table (or gone underneath it) • Before you change the y-position in update_position, add a check for this and manually set the y-position to 0 (I’ll explain why we do this later). • Inside this check you’ve added, we can know calculate energy and our new velocity!

17. Exercise 4 • To account for thermal energy, reduce the ball’s energy by 20% • energy *= 0.8 • You have your energy and mass, therefore you can solve this equation for velocity • Ek = ½ m*v2 • Math time! Solve the equation for v to get the equation you need. • Now set your y-velocity to this new velocity • Congratulations! You have successfully implemented a (quasi) realistic bouncing ball!

18. Sidenotes • Manually setting the position of the ball to 0 is an incorrect way of animating what’s really occurring. The correct way is to detect the instant the ball hits the table, and subtract that from your recorded delta time. • animation_t = delta_t – collision_t • Then, you can animate the ball bouncing up for this amount of time, and this will be the “realistic” way of animating your ball.

19. Questions?