Theoretical Principles & Computational Physics Guide
Python Lists: Dynamic Arrays & Trajectory Buffers
Dr. Alorika Chatterjee & Dr. Anirban Shaw
Science & Physics Learners
Python 3 / NumPy / SciPy
1. Core Principles & Theoretical Framework
Dynamic Sequences: Mutable sequences ideal for appending time-series coordinates during numerical simulations.
Slicing & Indexing: Expressive slicing (
x[::2], x[-10:]) allows efficient downsampling and inspection. List Comprehensions: Compact functional syntax for transforming coordinate arrays into energies.
2. Mathematical Formulation & Algorithmic Pipeline
Discrete trajectory state vector sequence:
$$ \mathbf{X} = [x_0, x_1, x_2, \dots, x_N], \quad E_k = \frac{1}{2}m v_k^2 + V(x_k) $$
3. Numerical Mechanics & Implementation Logic
- Buffer Initialization: Initialize empty lists (
t_list = [],x_list = []) before stepping loops. - State Appending: Record variables via
.append()at each integration interval. - Transformations: Convert lists to kinetic energies using list comprehensions:
[0.5 * m * v**2 for v in vel].
4. Relevant Computational Practice Exercises
Exercise 1
Simulate a free-falling body, accumulating height and velocity in lists, then plot $y$ vs $t$ using Matplotlib.
Exercise 2
Compute a 5-point moving average filter over a noisy experimental dataset stored in a list.
Exercise 3
Use list comprehension to compute the gravitational potential energy $U = mgh$ for a list of 100 height samples.
- Mark Newman, "Computational Physics", University of Michigan (2013).