Dynamics – gyan’s sight

problem01

1. Set up (define system, draw FBD, write ODEs) a particle problem. Just one particle. 2D or 3D, your choice. Use a force, or forces that you like (gravity, spring, air…

problem02

2. 3D. Get good at vectors. Assume that the positions relative to an origin of four random points, which are randomly located in space are given as \(\vec{\mathbf{r}}_A\), \(…

problem03

3. More ODE & animation practice. Take a simple set of ODEs. Use a set you like,e.g., harmonic oscillator, non-linear pendulum, the Lorentz system (look it up on the…

problem04

4. Cross product: geometry vs components.

problem05

5. Read up.

problem06

6. Spring and mass (2D). One end of of a negligible-mass spring (k, L0) is pinned to the origin, the other to a mass (m). There is gravity (g). Initial Conditions (ICs): The…

problem07

7. Simple animation of a shape. Draw a picture of some object (a face, a house, whatever), and make it move around on the screen in a smooth and interesting way. No…

problem08

8. Simplest dynamics with Polar coordinates. This is the simplest dynamics problem, but posed in polar coordinates. Assume a particle is on a plane with no force on it. So…

problem09

9. Canon ball. A cannon ball m is launched at angle θ and speed v0. It is acted on by gravity g and a viscous drag with magnitude \(\|c \vec{v}\|\).

problem10

10. Mass hanging from spring. 3D. Consider a point mass hanging from a zero-restlength linear spring (`0 = 0) in a constant gravitational field.

problem11

11. Central force. These two problems are both about central forces. In both cases the only force is central (directed on the particle towards the origin) and only depends…