Day 10 - Integrating EOMs Numerically

Announcements

  • PERMANENT CHANGE: OFFICE HOURS
    • DC Office hours 10:00-12:00 on Fridays (No Monday office hours)
  • CHANGES THIS WEEK (DC has a conflict):

Seminars this week

Astronomy Seminar, Wednesday Feb 5th at 1:30pm in 1400 BPS

  • Lia Corrales, Univ. of Michigan, The cosmic journey of the elements, from dust to life

Physics & Astronomy Colloquium, Thursday Feb 6th at 3:30pm in 1415 BPS

  • Andreas Jung, Purdue University, Entangled Titans: unraveling the mysteries of Quantum Mechanics with top quarks

Reminder: email me your extra credit seminar write-ups

Goals for this week

  • Establish a model for drag forces
  • Develop an understanding of the process for modeling forces
  • Produce equations of motion that can be investigated
  • Start probing the behavior of these systems with math and computing

Model-to-EOM Pipeline for Classical Mechanics

  1. ✅ Develop conceptual description of the system; make justifiable assumptions
  2. ✅ Using a framework of physics (i.e., Newton's Laws, Lagrangian Dynamics), develop a mathematical model of the system
  3. ✅ Produce the equations of motion (EOM) by following the framework (i.e., ordinary differential equations)
  4. 😵 Solve for trajectories of the system (e.g., , , )

Most EOMs are nonlinear

We need approximate methods to produce trajectories

Clicker Question 6-5

For the system of Quadratic Drag in 1D, we found a solution for the velocity as a function of time, with at .

where . What happens when ?

  1. The object stops moving.
  2. The object travels at a constant velocity.
  3. The object travels at an increasing velocity.
  4. The object travels at a decreasing velocity.
  5. I'm not sure.

Clicker Question 6-6

For the gravitational interaction, I want to compute the force acting on body B, located at , by body A, located at .

The gravitational force is given by:

What is the appropriate form of ?

  3. Either is ok

Clicker Question 6-7

We found that the equation of motion for the spring-mass system was:

Your friends have proposed the following general solutions:

How many of them are correct?
(1) Only one (2) Two (3) Three
(4) Four (5) All of them