Chaos Derived solution for Artificial Gravity Multiple models

Simulated Gravity Generation via Chaotic Oscillator Systems with Auxiliary Energy Harvesting

Description:

This project presents a simulation framework for generating consistent artificial gravity using chaotic motion systems. The simulation evaluates three nonlinear dynamic models—double pendulum, Duffing oscillator, and a simplified triple pendulum—as sources of modulated force output to stabilize and regulate a gravity-like experience.

The central aim is to maintain a target gravitational force (matching Earth’s gravity at ~9.81 m/s²) on a simulated platform by dynamically adjusting force output derived from the controlled chaotic motion of these systems. This is achieved using predictive modeling, regulated feedback loops, and adaptive control of oscillatory force amplitudes.

Although the system includes a mechanism for harvesting kinetic energy during high-motion events (i.e., chaotic spikes), this is a secondary feature intended to demonstrate that such systems, when tuned properly, may offer energy efficiency benefits.

Primary Objectives:

• Artificial Gravity Simulation
  Maintains a consistent gravitational force through chaotic motion modulation using mechanical systems without relying on rotation or centrifugal force.

• Chaotic Oscillator Models
  Simulates gravity-stabilizing force output using:

  • Double Pendulum

  • Duffing Oscillator

  • Simplified Triple Pendulum

• Force Regulation & Feedback Control
  Dynamically smooths force output using oscillatory gain adjustment, force error correction, and spike prediction suppression.

• Performance Tracking
  Logs platform acceleration, total mechanical energy, and force output stability across all models.

Secondary Features:

• Energy Harvesting Logic
  Opportunistically captures excess chaotic energy during spike events with defined harvesting efficiency and cooldown logic.

• Energy Conservation Analysis
  Compares system input versus output energy to analyze efficiency and system stability under different dynamic regimes.

• Frequency Analysis
  Applies Fast Fourier Transform (FFT) to acceleration data to assess the frequency stability and signal purity of generated gravity.

Mathematical Modeling:

The simulation uses:

• Lagrangian equations for the double pendulum to model angular velocity and acceleration across joints

• Nonlinear differential equations for the Duffing oscillator:

  x¨+0.25x˙+x−x3=0.3cos⁡(1.2t)\ddot{x} + 0.25 \dot{x} + x - x^3 = 0.3 \cos(1.2t)x¨+0.25x˙+x−x3=0.3cos(1.2t)

• Custom simplified dynamic rules for triple pendulum emulation

Gravitational output is regulated around a target net force:

Fnet=m⋅g+chaotic force correctionsF_{\text{net}} = m \cdot g + \text{chaotic force corrections}Fnet=m⋅g+chaotic force corrections

with bounded error correction and system-state tracking for cooldown and stability.

Outputs and Deliverables:

• Time-series plots of gravitational force stability

• Mechanical energy curves for all models

• Acceleration frequency spectra

• Side-by-side comparisons of all three systems

• Timestamped directory containing all result files and charts