Placed in or among, as if woven together.
Used in a Sentence
symplectic
Definitions, parts of speech, synonyms, and sentence examples for symplectic.
Editorial note
This is typically handled by choosing a solver that maintains such invariants by construction, e.g., symplectic methods for Hamiltonian systems conserve symplectic 2-form.
Examples18
Definitions4
Parts of speech2
Quick take
Placed in or among, as if woven together.
Meaning at a glance
The clearest senses and uses of symplectic gathered in one view.
That moves in the same direction as a system of synchronized waves.
(mathematics) A symplectic bilinear form, manifold, geometry, etc.
Definitions
Core meanings and parts of speech for symplectic.
adjective
Placed in or among, as if woven together.
adjective
That moves in the same direction as a system of synchronized waves.
noun
(mathematics) A symplectic bilinear form, manifold, geometry, etc.
adjective
(mathematics, multilinear algebra, of a bilinear form) That is alternating and nondegenerate.
Example sentences
This is typically handled by choosing a solver that maintains such invariants by construction, e.g., symplectic methods for Hamiltonian systems conserve symplectic 2-form.
But there are still many applications where you for example want to use symplectic methods instead.
Anyway, a symplectic integrator [1] would be more suitable for this problem, since it has the beautiful property of conserving energy.
The solution is to use a geometric or sympletic integrator which explicitly takes into account the symplectic structure, producing a set of discrete update equations which still conserve a total energy quantity.
That falls into the class of symplectic integrators, so it should handle SE(3) fine.
Use an adaptive symplectic integrator and get the best of both worlds.
I'm tempted now to write a symplectic integrator and see how it performs against adaptive RK4.
They tell you that symplectic methods are great for time reversible problems.
Curiously, the comparisons I've seen between RK4 and symplectic integrators all use fixed step sizes.
It is a simple leapfrog integrator (which is indeed symplectic).
It may be better to use a symplectic integrator.
There are symplectic variants of Runge-Kutta too.
Quote examples
Maybe I'll build a symplectic integrator in future, but this was a case of "Hey, I've got this hammer, maybe I can drive this screw with it!"
If scientific accuracy is required, gravity simulations are usually done with "symplectic" integrators (which don't "lose" energy) and the equations of motion are written using Hamiltonian mechanics.
This was also colloquially known as the "leapfrog" algorithm and is the simplest of a class of integrators that are symmetric (in simulation time) and symplectic which are crucial properties for some simulations.
Proper noun examples
Symplectic geometry in vector space R^2 is used here as a new approach and leads to some new recursive vector formulas.
Symplectic integrators are the approach I used for some old galaxy simulations.
Symplectic geometry is a bit more abstract.
Frequently asked questions
Short answers drawn from the clearest meanings and examples for this word.
How do you use symplectic in a sentence?
This is typically handled by choosing a solver that maintains such invariants by construction, e.g., symplectic methods for Hamiltonian systems conserve symplectic 2-form.
What does symplectic mean?
Placed in or among, as if woven together.
What part of speech is symplectic?
symplectic is commonly used as adjective, noun.