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SciCode / 78 / Chaotic_Dynamics_Pendulum

Problem

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problem description main

You are tasked with conducting a detailed study of a damped, driven pendulum system to understand its dynamic behavior under various conditions. This study aims to explore the impact of different damping coefficients, driving forces, and timestep sizes on the system's stability and motion. You will also investigate the chaotic behavior and analyze the global truncation error (GTE) to ensure accurate numerical solutions.

problem name

Chaotic_Dynamics_Pendulum

problem background main

problem io
"""
Inputs:
g: Acceleration due to gravity, float.
L: Length of the pendulum, float.
beta: Damping coefficient, float.
A: Amplitude of driving force, float.
alpha: Frequency of driving force, float.
initial_state: Initial state vector [theta, omega], list of floats.
t0: Initial time, float.
tf: Final time, float.
min_dt: Smallest timestep, float.
max_dt: Largest timestep, float.
num_timesteps: Number of timesteps to generate, int.

Outputs:
optimized_trajectory:numpy array of floats, The trajectory of the pendulum system using the optimized timestep.
"""
required dependencies
import numpy as np
import time
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Source and history
upstream_id / Original problem ID
78
task_id
831ff049-2748-5e6d-ba9b-f8252555cd23
task_key
dev--78
task_revision_id
5
config / split
 / dev
Official source
initial import