Satellite Ground Tracks

The ground track of a satellite is its orbit projected into the surface. I’d recommend checking out the post on astrodynamics first, which gives a basic overview of how orbits work.

Low Thrust Transfers

In general, there is no way to algebraically solve for a low thrust trajectory. Instead, for problems of this type we need to solve for x(t) and u(t) through trajectory optimization. However, this can be a lengthy process, especially if done without other engineering constraints.

Astrodynamics

Astrodynamics is a lot like any other field of dynamics, except we now have an additional equation to consider: the law of universal gravitation. This leads to some strange and counterintuitive results - like slowing down to catch up!

Intro to Control Theory

In previous posts, we explored the field of dynamics, which taught us how to calculate the position, velocity, and acceleration of an object given a set of driving forces. The topic of control theory flips this process around, and seeks an answer to the question: what type of force will produce the desired motion? In other words, if dynamics is the study of rules, controls is the study of how we use those rules to achieve results.

Fundamentals of Dynamics

In dynamics, the goal is to predict the position, velocity, and acceleration of rigid bodies as a function of time through using this equation: F=ma. While the basic principle is simple, the key challenge of dynamics involves defining reference frames, vectors, and their relationships.

Note that F = ma is not the only way to solve dynamics problems! In the late 1700’s, Joseph-Louis Lagrange introduced an energy conservation strategy, known today as the Euler-Lagrange Equations.

Kinematics

A subset of dynamics, where forces are neglected, and we focus instead on the motion of points and rigid bodies over time. At the core of this topic are a series of rules about positions, velocities, accelerations, and how to find them amid a potentially messy system of reference frames and motion constraints.

Finally Getting to Dynamics

We’re almost ready to write down F = ma, but before that, we need to define what F is (a force), and what ma is (an inertial term).