Orbital Mechanics with MATLAB
Welcome
This web site describes a comprehensive collection of MATLAB
scripts and functions called Orbital Mechanics with MATLAB. This software can be used to solve a variety
of practical problems in orbital mechanics and applied astrodynamics. MATLAB Scripts and functions are provided for
solving spaceflight problems in the areas of orbit design, event prediction and
trajectory optimization. All scripts and
support functions require MATLAB version 7.2 (R2006a) or higher.
The complete collection of MATLAB scripts and functions can be
purchased for $179. The software can be ordered using the
secure and flexible e-commerce services provided by PayPal (www.paypal.com). PayPal accepts online payments by
credit card and a PayPal account is not required to make a purchase. Before placing an order, please read the license agreement.
After placing your order, you will receive an email within 24 hours
with a password that will permit you to extract the MATLAB source code and any
support data files.
Click
here to order the complete software suite ($179).
The password protected zipped file for Orbital Mechanics with MATLAB can be downloaded here.
Last updated
January 15,
2013
Thanks for visiting.
The
following is a list of the analysis scripts and functions included in the complete
software suite. Click on the title to
view or download the PDF documentation.
Many of these MATLAB scripts and support functions are available in the
file exchange area of the Mathworks website, www.mathworks.com/matlabcentral/fileexchange/authors/30927.
·
Greenwich
mean and apparent sidereal time
·
Geodetic
and geocentric coordinates
·
Inertial
position and velocity vectors
·
Classical
orbital elements
·
Modified
equinoctial orbital elements
·
Hyperbolic
and B-plane coordinates
·
Flight
path coordinates
·
Topocentric
coordinates
·
Moon-centered
coordinate transformations
·
Mars-centered
coordinate transformations
·
EME
to/from true-of-date transformation
Orbital
Periods of a Satellite
·
Keplerian – the unperturbed or two-body period
·
Nodal – the time interval from one ascending (or descending)
node to the next
·
Anomalistic – the time interval from one perigee to
the next
·
Sidereal – the time interval from one value of argument of
latitude to the next identical value
·
Perturbed orbital motion of Earth satellites
·
Perturbed orbital motion of Earth satellites using MICE routines
·
Heliocentric orbit propagation
·
Drag perturbed orbital motion
·
Modified equinoctial equations of motion
·
Geocentric
orbits
·
Heliocentric
orbits
Rise and Set
of Earth Satellites
·
Kozai orbit
propagation
·
SGP4 orbit
propagation
·
Numerically
integrated orbital motion
·
Graphics
display of visibility conditions
Shadow
Conditions of Earth Satellites
·
Shadow
conditions of Earth satellites in circular orbits
·
Shadow
conditions using Kozai orbit propagation
·
Shadow
conditions using numerically integrated orbital motion
·
Lunar
eclipse of Earth satellites
·
Repeating
ground track orbits
·
Time to
repeat ground track – Kozai orbit propagation
·
Time to
repeat ground track – numerical integration
·
Repeating
ground track – required mean semimajor axis –
Wagner’s algorithm
·
Repeating
ground track – Required osculating semimajor axis –
numerical integration
·
Sun-synchronous
orbit – required mean orbital inclination – Kozai j2
solution
·
Sun-synchronous
orbit – required mean orbital inclination – Kozai
j2+j4 solution
·
Sun-synchronous
orbit – required osculating orbital inclination – numerical integration
·
Frozen
orbit – required mean orbital eccentricity
·
Long-term
evolution of frozen orbits
·
Sun-synchronous,
repeating ground track orbit
·
Sun-synchronous,
repeating ground track orbit, frozen orbit design
·
Equilibrium
longitudes and radii of geosynchronous satellites
·
Geosynchronous
orbit – required osculating semimajor axis
·
Repositioning
a geosynchronous satellite
·
East-west
station keeping of geosynchronous satellites
·
North-south
station keeping of geosynchronous orbits
Predicting
Mutual Visibility and Close Approach Conditions
·
Mutual
visibility between two satellites
·
Closest
approach between two satellites
·
Circular
orbit plane change
·
Single
impulse transfer between intersecting orbits
·
Finite
burn orbit transfer
·
Low thrust
orbit transfer
·
Low thrust
orbit transfer using solar-electric propulsion
·
Single impulse
de-orbit from a circular orbit
·
Single
impulse de-orbit from an elliptical orbit
·
Optimal
single impulse de-orbit from Earth orbits (SNOPT)
·
Aero-assisted
co-planar orbital transfer
·
Hohmann two
impulse orbital transfer
·
Bi-elliptic
transfer between coplanar circular orbits
·
Low-thrust
spiral trajectories with constant periapsis radius
·
Primer
vector analysis
·
Phasing
analysis
·
Earth
orbit solution
·
Interplanetary
solution
·
Earth
orbit solution – perturbed orbital motion – shooting method
·
Earth
orbit solution – perturbed orbital motion – NLP method
Coverage
Characteristics of Earth Satellites
·
Geometry of
satellite coverage
·
Coverage
characteristics of satellite constellations
·
Long-term
prediction of view periods
Relative
Motion Between Two Earth Satellites
·
Relative
motion of two Earth satellites in circular orbits
·
Two
impulse rendezvous orbit
Circular-Restricted
Three-Body Problem
·
Coordinates
and energy of the libration points
·
Graphics
display of three-body motion
·
Graphics
display of zero velocity curves
·
Graphics
display of user-defined zero relative velocity
Graphics
Display of Satellite Ground Tracks, Orbits and Maps
·
ground track – rectangular display
·
orbit and/or ground track – orthographic display
·
site-to-satellite visibility – azimuth/elevation polar plot
·
site-to-satellite visibility – rectangular display
·
site-to-satellite visibility – orthographic display
Numerical
Methods and Utility Functions
·
Trigonometry
and matrix routines
·
Solution
of first and second-order systems of differential equations
·
Quadrature
(numerical integration)
·
One-dimensional
root-finding and minimization
·
Linear and
cubic spline Interpolation functions
·
Date and
time routines
·
Interactive
data request routines
·
Kepler’s equation
·
Two-body
orbital motion (initial value problem)
·
Analytic
orbit propagation functions
·
Two-body
state transition matrix
·
Differential
equations of orbital motion
·
Lambert’s
problem (two-point boundary value problem)
·
Mean and
osculating orbital elements
·
Predicting
trajectory events
·
Earth
atmosphere models
·
Atmosphere
and gravity model data files
·
Low precision solar, lunar and planetary ephemeris
·
Precision sun ephemeris
·
Osculating orbital elements of the moon
·
Mean planetary ephemerides
·
J2000 planetary ephemerides
·
IMCCE lunar and planetary ephemeris
·
JPL lunar and planetary ephemeris
·
INPOP06C binary ephemeris
·
Ephemeris of a heliocentric celestial body
·
Apparent coordinates of the moon, planet and star
Numerical Prediction
of Orbital Events
·
geodetic
altitude
·
geodetic
latitude
·
east
longitude
·
geocentric
declination
·
true
anomaly
·
argument
of latitude
·
flight
path angle
·
orbital
speed
·
right
ascension
Aerospace
Trajectory Optimization Using Direct Transciption
(SNOPT)
This brief
report describes a technical approach and MATLAB script that demonstrate the
use of direct transcription and collocation to solve aerospace optimal
control problems. The computer program
solves the problem described on pages 66-69 of the classic text, Applied Optimal Control, by Arthur E.
Bryson, Jr. and Yu-Chi Ho.
PLEASE NOTE: The MATLAB scripts flagged with SNOPT were
written for use with the SNOPT nonlinear programming (NLP) algorithm. MATLAB versions of SNOPT for several computer
platforms can be found at Professor Philip Gill’s web site which is located at http://scicomp.ucsd.edu/~peg/. A PDF version of the SNOPT user’s manual is
also available at that website. These
scripts have been tested with Windows XP Professional (32 bit), Windows 7 Home
Premium (32 bit), versions R2010a and R2010b of MATLAB, and the 12/30/2010
version of SNOPT.
DOWNLOADS
(The
following scripts and support functions are available in the file exchange area of the Mathworks website, www.mathworks.com/matlabcentral/fileexchange/authors/30927.)
A MATLAB Script for
Designing Low-thrust Spiral Trajectories with Constant Periapsis
Radius
Bi-elliptic Transfer Between Coplanar Circular Orbits
Optimal Single Impulse
De-orbit from Earth Orbits
Demo Script for Hyperbolic
Coordinates
Demo Script for
Calculating Sidereal Time with NOVAS 3.0
Please note that these binary
ephemeris files are compatible with Windows computers.
SLP96 ephemeris binary
data file (~6 MB)
JPL DE405
ephemeris binary data file (~6 MB)
JPL DE421
ephemeris binary data file (~14 MB)
INPOP06c
ephemeris binary data file (~17 MB)
INPOP08a
ephemeris binary data file (~17 MB)
(These
functions are available
in the file exchange area of the Mathworks website, www.mathworks.com/matlabcentral/fileexchange/authors/30927.)
These scripts
illustrate several applications of the JPL MICE library. MICE is a MATLAB
implementation of many of the JPL SPICE routines. Additional information about MICE and SPICE
along with downloadable software and documentation can be found at http://naif.jpl.nasa.gov/naif/.
(The
following scripts and support functions are available in the file
exchange area of the Mathworks website, www.mathworks.com/matlabcentral/fileexchange/authors/30927.)
This
script is a MICE version of Cowell’s method for geocentric spacecraft.
Output text file (example.txt)
This
script computes the state vector of the Moon at the DE405 integration epoch .
Output text file (de405_integration_epoch.txt)
This
script performs the EME to/from true-of-date transformation .
Output text file (eme_tod_mice.txt)
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site contents copyright © 1996-2013 by C. David Eagle. All rights reserved.
cdeaglejr@yahoo.com www.cdeagle.com