This project is a simulation of a time-step-driven system. The system is composed of a set of components that interact with each other. The simulation is driven by a time-step mechanism, where each component is updated at each time step. Three integration methods are implemented: Verlet, Beeman and Gear Predictor-Corrector. The system that is simulated is a solar system with the Sun, the Earth, Mars and, optionally, Jupiter. A spaceship is launched from Earth and it is studied how the spaceship is affected by the gravitational forces of the planets and the Sun.
- Java 19
- Maven
- Python 3 (only if you want the animation to be rendered)
To build the project, cd to the root of the project and run the following command:
mvn clean packageThis will compile and package a .jar file in the target directory.
Note
The following instructions assume that you have built the project as described in the previous section and that the generated .jar file is in the current working directory.
java -jar ss-tp4-1.0-SNAPSHOT.jar {{ executable }}Where {{ executable }} can be oscillator, mars or jupiter.
The program will execute the simulation of a simple harmonic oscillator with each of the three integration methods.
It will generate a series of output files named {{ method }}-{{ run }}.txt in the current working directory. Each run will have a different delta t, from the following list:
Each file will have the following structure:
{{ time }} {{ position }} {{ velocity }}
...
The program will execute the simulation of the solar system with the Sun, the Earth and Mars. The spaceship will be launched from Earth and its trajectory will be studied.
The program expects to have an input file named input.txt in the current working directory. The input file should contain the following structure:
{{ sun_mass }}
{{ sun_radius }}
{{ earth_mass }}
{{ earth_radius }}
{{ earth_x }}
{{ earth_y }}
{{ earth_vx }}
{{ earth_vy }}
{{ mars_mass }}
{{ mars_radius }}
{{ mars_x }}
{{ mars_y }}
{{ mars_vx }}
{{ mars_vy }}
{{ spaceship_mass }}
{{ spaceship_initial_distance_to_earth }}
{{ spaceship_initial_velocity }}
Where:
sun_massis the mass of the Sun.sun_radiusis the radius of the Sun.earth_massis the mass of the Earth.earth_radiusis the radius of the Earth.earth_xis the x-coordinate of the Earth.earth_yis the y-coordinate of the Earth.earth_vxis the x-component of the velocity of the Earth.earth_vyis the y-component of the velocity of the Earth.mars_massis the mass of Mars.mars_radiusis the radius of Mars.mars_xis the x-coordinate of Mars.mars_yis the y-coordinate of Mars.mars_vxis the x-component of the velocity of Mars.mars_vyis the y-component of the velocity of Mars.spaceship_massis the mass of the spaceship.spaceship_initial_distance_to_earthis the distance between the spaceship and Earth when it is launched.spaceship_initial_velocityis the initial velocity of the spaceship, tangent to the Earth.
This will generate an output file named mars_mission.txt in the current working directory, with the following structure:
{{ time }} {{ earth_x }} {{ earth_y }} {{ mars_x }} {{ mars_y }} {{ spaceship_x }} {{ spaceship_y }} {{ earth_vx }} {{ earth_vy }} {{ mars_vx }} {{ mars_vy }} {{ spaceship_vx }} {{ spaceship_vy }}
...
The program will execute the simulation of the solar system with the Sun, the Earth, Mars and Jupiter. The spaceship will be launched from Earth and its trajectory will be studied.
The program expects to have an input file named jupiter_input.txt in the current working directory. The input file should contain the following structure:
{{ sun_mass }}
{{ sun_radius }}
{{ earth_mass }}
{{ earth_radius }}
{{ earth_x }}
{{ earth_y }}
{{ earth_vx }}
{{ earth_vy }}
{{ mars_mass }}
{{ mars_radius }}
{{ mars_x }}
{{ mars_y }}
{{ mars_vx }}
{{ mars_vy }}
{{ jupiter_mass }}
{{ jupiter_radius }}
{{ jupiter_x }}
{{ jupiter_y }}
{{ jupiter_vx }}
{{ jupiter_vy }}
{{ spaceship_mass }}
{{ spaceship_initial_distance_to_earth }}
{{ spaceship_initial_velocity }}
Where:
sun_massis the mass of the Sun.sun_radiusis the radius of the Sun.earth_massis the mass of the Earth.earth_radiusis the radius of the Earth.earth_xis the x-coordinate of the Earth.earth_yis the y-coordinate of the Earth.earth_vxis the x-component of the velocity of the Earth.earth_vyis the y-component of the velocity of the Earth.mars_massis the mass of Mars.mars_radiusis the radius of Mars.mars_xis the x-coordinate of Mars.mars_yis the y-coordinate of Mars.mars_vxis the x-component of the velocity of Mars.mars_vyis the y-component of the velocity of Mars.jupiter_massis the mass of Jupiter.jupiter_radiusis the radius of Jupiter.jupiter_xis the x-coordinate of Jupiter.jupiter_yis the y-coordinate of Jupiter.jupiter_vxis the x-component of the velocity of Jupiter.jupiter_vyis the y-component of the velocity of Jupiter.spaceship_massis the mass of the spaceship.spaceship_initial_distance_to_earthis the distance between the spaceship and Earth when it is launched.spaceship_initial_velocityis the initial velocity of the spaceship, tangent to the Earth.
This will generate an output file named jupiter_mission.txt in the current working directory, with the following structure:
{{ time }} {{ earth_x }} {{ earth_y }} {{ mars_x }} {{ mars_y }} {{ jupiter_x }} {{ jupiter_y }} {{ spaceship_x }} {{ spaceship_y }} {{ earth_vx }} {{ earth_vy }} {{ mars_vx }} {{ mars_vy }} {{ jupiter_vx }} {{ jupiter_vy }} {{ spaceship_vx }} {{ spaceship_vy }}
...
Note
The following instructions assume that you have executed the project as described in the previous section and that all he output files are in the current working directory.
To visualize the output, we must run a Python script. First, we need to install the required dependencies. To do so, run the following command:
python -m venv venv
source venv/bin/activate
pip install -r animation/requirements.txtTo visualize the output of the oscillator, run the following command:
python animation/oscillator.pyThis will generate a plot with the position of the oscillator as a function of time for each integration method, as well as the analytical solution.
To visualize the error of each integration method as a function of delta t, run the following command:
python animation/oscillator_error_vs_dt.pyThis will generate a plot with the error of each integration method as a function of delta t. The calculated error is the mean squared error between the analytical solution and the numerical solution.
To visualize the Mars mission animation, run the following command:
python animation/mars_animation.pyThis will generate an animation of the solar system with the Sun, the Earth, Mars and the spaceship. The animation will show the trajectory of the spaceship as it is launched from Earth.
To visualize the Jupiter mission animation, run the following command:
python animation/jupiter_animation.pyThis will generate an animation of the solar system with the Sun, the Earth, Mars, Jupiter and the spaceship. The animation will show the trajectory of the spaceship as it is launched from Earth.
- Minimum distance to Mars vs launch day:
python animation/distance_to_mars_vs_departure_day.py - Minimum distance to Jupiter vs launch day:
python animation/distance_to_jupiter_vs_departure_day.py - Travel time vs initial velocity for a Mars mission:
python animation/travel_time_vs_initial_velocities.py - Travel time vs initial velocity for a Jupiter mission:
python animation/jupiter_travel_time_vs_initial_velocities.py - Spaceship velocity vs time:
python animation/spaceship_velocity_vs_time.py - Universe energy vs time:
python animation/universe_energy_vs_time.py
This project was done in an academic environment, as part of the curriculum of Systems Simulation from Instituto Tecnológico de Buenos Aires (ITBA).
The project was carried out by:
- Alejo Flores Lucey
- Nehuén Gabriel Llanos