69 lines
2.5 KiB
Markdown
69 lines
2.5 KiB
Markdown
# 3D Gravity Simulato
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## Overview
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This 3D Gravity Simulator is a C++ program that visualizes the gravitational interactions between celestial bodies in a simplified solar system model. It uses OpenGL for rendering and GLFW for window management and user input.
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## Program Structure
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The simulator consists of several key components:
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1. `Simulator`: Handles the physics calculations and updates the positions of celestial bodies.
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2. `Renderer`: Manages the 3D rendering of the celestial bodies, trajectories, and grid.
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3. `CelestialBody`: Represents individual celestial bodies with properties like mass, position, and velocity.
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## Physics Implementation
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### Gravitational Force
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The simulator uses Newton's law of universal gravitation to calculate the forces between celestial bodies. The gravitational force between two bodies is given by:
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$$
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F = G \frac{m_1 m_2}{r^2}
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$$
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Where:
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- $F$ is the gravitational force between the two bodies
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- $G$ is the gravitational constant ($6.67430 \times 10^{-11} \, \text{N} \cdot \text{m}^2 / \text{kg}^2$)
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- $m_1$ and $m_2$ are the masses of the two bodies
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- $r$ is the distance between the centers of the two bodies
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### Motion Update
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The motion of each celestial body is updated using numerical integration. We use a simple Euler method for updating positions and velocities:
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1. Calculate the net force on each body
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2. Calculate acceleration:
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```math
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$$ \vec{a} = \frac{\vec{F}}{m} $$
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```
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3. Update velocity:
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```math
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$$ \vec{v}_{new} = \vec{v}_{old} + \vec{a} \Delta t $$
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```
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4. Update position:
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```math
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$$ \vec{x}_{new} = \vec{x}_{old} + \vec{v}_{new} \Delta t $$
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```
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Where $\Delta t$ is the time step of the simulation.
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## Rendering
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The program uses OpenGL to render the 3D scene:
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- Celestial bodies are represented as spheres with sizes proportional to their masses (using a logarithmic scale).
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- A grid is drawn to provide a reference plane.
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- Trajectories of the bodies are drawn as lines, fading out over time.
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- The camera can be controlled using WASD keys for movement and the mouse for orientation.
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## Limitations and Simplifications
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1. The simulation uses a fixed time step, which can lead to inaccuracies in long-term simulations.
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2. The Euler method for numerical integration is simple but can accumulate errors over time.
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3. The scale of the celestial bodies and their distances are not to true scale to make visualization easier.
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4. Relativistic effects are not considered; the simulation uses classical Newtonian mechanics.
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