Dynamics – gyan’s sight

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This page lists all of the homework solutions to a set of problems in Dynamics and Simulations. I have used the Julia Programming Language.

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…

problem12

12. Canon ball 2. A cannon ball \(m\) is launched at angle \(\theta\) and speed \(v_0\). It is acted on by gravity \(g\) and a quadratic drag with magnitude \(\|cv^2\|\).

problem13

13. Statics vs Dynamics. 2D. Equilibrium and dynamics of a point mass \(m\) at \(\vec{r}_{C}\). Gravity \(g\) points down in the minus \(\hat{j}\) direction. Points A and B…

problem14

What means “rate of change of angular momentum”? Consider a moving particle P. Consider also a moving point C (moving relative to a Newtonian frame \(\mathcal{F}\) that has…

problem15

15. Potential Energy. For each of the force fields below, find the associated potential energy function. All of them are 3D. In some cases the energy is associated with the…

problem16

16. Mechanics of two or more particles

problem17

17. Montgomery’s eight. (From Ruina/Pratap). Three equal masses, say \(m = 1\), are attracted by an inverse-square gravity law with \(G = 1\). That is, each mass is…

problem18

18. Konig’s Theorem. The total kinetic energy of a system of particles is

problem19

19. What means “rate of change of angular momentum” for a SYSTEM of particles? You should master problem 14 before looking at this problem. Consider a system of moving…

problem20

20. Two masses. This problem has 3 independent educational goals: