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Main
Installation
Changelog
Breaking changes
Benchmarks
Acknowledgement
Tutorials
Basic
Taylor’s method
Introduction to the expression system
The adaptive integrator
Customising the adaptive integrator
ODEs with parameters
Non-autonomous systems
Dense & continuous output
Event detection
Variational ODEs
The expression system
Common pitfalls
Computing derivatives
Supporting large computational graphs
Advanced
Batch mode
Ensemble propagations
Parallel mode
Computations in extended precision
Computations in arbitrary precision
Computations in single precision
Lagrangian and Hamiltonian mechanics
Interoperability with SymPy
Compiled functions
Pickle support
JIT compilation and caching
Examples
Celestial mechanics and astrodynamics
The restricted three-body problem
Continuation of Periodic Orbits in the CR3BP
Pseudo arc-length continuation in the CR3BP
Brouwer’s law in the outer Solar System
Long term stability of N-body simulations: the case of Trappist-1
Conserving first integrals via manifold projection
Box control in satellite Formation Flying
Comparing coordinate systems
Inverting Kepler’s equation in ODEs
Planetary embryos in the inner Solar System
Mercury’s relativistic precession
Calculating transit timing variations
Introduction to the VSOP2013 planetary theory
Introduction to the ELP2000 lunar theory
Elastic tides
Lagrange propagation and the state transition matrix
Gravity-gradient stabilization
A differentiable SGP4 propagator
Event detection
Sampling events
Poincaré sections
The second integral of motion
The Keplerian billiard
The two-fixed centres elliptic billiard
The wavy ramp
The Maxwell-Boltzmann distribution
Computing event sensitivity
Machine Learning
Feed-Forward Neural Networks
Interfacing
torch
to
heyoka.py
Neural ODEs
Neural Hamiltonian ODEs
ThermoNETs
Differentiable Atmosphere
Variational equations
Jet transport in the simple pendulum
Learning mass distributions in asteroids
Map inversion and event sensitivities
The Tolman–Oppenheimer–Volkoff equations (Lindblom’s form)
Others
Evaluating the performance of ensemble & batch mode
The variational equations
Optimal Control of the Lotka-Volterra equations
Computing definite integrals
API reference
Common keyword arguments
Expression system
heyoka.expression
heyoka.dtens
heyoka.make_vars
heyoka.diff_tensors
heyoka.subs
heyoka.sum
heyoka.prod
heyoka.par
heyoka.time
heyoka.diff_args
Numerical integrators
heyoka.taylor_adaptive
Variational ODE systems
heyoka.var_ode_sys
heyoka.var_args
Lagrangian and Hamiltonian mechanics
heyoka.lagrangian
heyoka.hamiltonian
Models
heyoka.model.sgp4_propagator_dbl
heyoka.model.sgp4_propagator_flt
heyoka.model.cart2geo
heyoka.model.nrlmsise00_tn
heyoka.model.jb08_tn
heyoka.model.fixed_centres
heyoka.model.pendulum
heyoka.model.sgp4
heyoka.model.sgp4_propagator
JIT compilation
heyoka.code_model
Repository
Open issue
.rst
.pdf
Numerical integrators
Numerical integrators
#
taylor_adaptive
(sys[, state])
