Vulcan Comprehensive Demo Guide

This guide details the comprehensive engineering examples included in examples/comprehensive/. These demos showcase how to combine Vulcan's modules (Dynamics, Aerodynamics, Orbital, Propulsion) with Janus's dual-mode numeric/symbolic architecture to solve complex aerospace problems.

Overview of Demos

Demo	File	Key Features
Rocket Ascent	comprehensive_ascent.cpp	trajectory optimization, variable mass, aerodynamic heating constraint, custom constraints
Hypersonic Reentry	hypersonic_reentry.cpp	bank angle modulation, thermal constraints, cross-range maximization, USSA-76 atmosphere
Lunar Transfer	lunar_transfer.cpp	porkchop plots, orbital mechanics, analytical ephemeris, delta-v budgeting
Slosh Stability	slosh_stability.cpp	coupled rigid-flexible dynamics, frequency domain filtering, autopilot gain optimization

1. Rocket Ascent Trajectory (comprehensive_ascent.cpp)

Goal: Maximize payload to orbit by optimizing the pitch profile.

Physics

• Propulsion: Tsiolkovsky rocket equation with gravity losses.
• Aerodynamics: Drag ($C_d$) and Max-Q constraints.
• Environment: Exponential atmosphere model.

Key Concepts

• Hybrid Optimization: Uses a numeric sweep to find a good initial guess for the pitchover altitude, then symbolically optimizes the parameters.
• Graph Export: detailed plots of Altitude, Velocity, and Dynamic Pressure.

Usage

./build/examples/comprehensive/comprehensive_ascent

2. Hypersonic Reentry (hypersonic_reentry.cpp)

Goal: Maximize cross-range for a reentering vehicle by modulating bank angle.

Physics

• Dynamics: 3-DOF guided point mass equations (Gamma-dot, Chi-dot).
• Thermal: Stagnation point heating rate scaling with $\sqrt{\rho} v^3$.
• Atmosphere: vulcan::atmosphere::ussa1976 for realistic density profiles.

Key Concepts

• Path Constraints: Constrains maximum heating rate and dynamic pressure during the trajectory.
• Symbolic Integration: Demonstrates integrating complex equations of motion symbolically for gradient-based optimization.

Usage

./build/examples/comprehensive/hypersonic_reentry

3. Lunar Transfer (lunar_transfer.cpp)

Goal: Find the minimum Delta-V transfer to the Moon for a given launch window.

Physics

• Orbital Mechanics: Patched conics approximation.
• Transfer: Hohmann transfer approximation modified for non-coplanar/elliptical targets.
• Ephemeris: Analytical breakdown of Moon's position relative to Earth.

Key Concepts

• Porkchop Plot: Generates specific Delta-V data across a grid of departure dates and flight times to visualize launch windows.
• Units: extensive use of vulcan::orbital constants and conversion factors.

Usage

./build/examples/comprehensive/lunar_transfer

4. Slosh-Coupled Roll Control (slosh_stability.cpp)

Goal: Design a roll autopilot that is stable despite fuel sloshing.

Physics

• Coupled Dynamics:
  • Rigid body roll dynamics ($I \ddot{\phi} = M$)
  • Pendulum slosh model ($\ddot{\theta} + 2\zeta\omega
    {\theta} + \omega^2\theta = -\ddot{\phi}/r$)