# Integrator type in order to solve the differential equations [closed]

Hi,

Does anyone know which integrator type (e.g. implicit Euler) is used in Gazebo, respectively ODE, in order to solve the differential equations?

Best Nils

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### Closed for the following reason the question is answered, right answer was accepted by NRottmann close date 2017-10-06 05:44:14.869176

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Gazebo uses ODE as physics engine by default and ODE uses semi-implicit Euler integration. Bullet uses semi-implicit Euler integration as well.

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Hi, thanks for your answer. Do you know where I can find some paper or something else where the integrator type of the ODE is described?

( 2017-10-02 03:19:38 -0500 )edit
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You can probably refer to this webpage: http://wiki.ros.org/physics_ode/ODE although the latex display is bad, but you might get an idea. If you are looking for how the time stepper is working, refer to my thesis here https://foswiki.cs.rpi.edu/foswiki/pub/RoboticsWeb/LabPublications/YLu_thesis.pdf In chapter 3, From basic equation of motion (3.1), you can jump to equation (3.27) Hopefully section 3.3 in this thesis will give you some reference as well

( 2017-10-04 11:11:46 -0500 )edit

From the ODE manual (https://www.ode-wiki.org/wiki/index.p...):

"ODE uses a first order semi-implicit integrator. The "semi implicit" means that some forces are calculated as though an implicit integrator is being used, and other forces are calculated as though the integrator is explicit. The constraint forces (applied to bodies to keep the constraints together) are implicit, and the "external" forces (applied by the user, and due to rotational effects) are explicit. Now, inaccuracy in implicit integrators is manifested as a reduction in energy - in other words the integrator damps the system for you. Inaccuracy in explicit integrators has the opposite effect - it increases the system energy. This is why systems simulated with explicit first order integrators can explode."

Searching for integrator in the manual turns up other tidbits regarding ODE's integration behavior.

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Thanks a lot for your answers :)

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Asked: 2017-09-28 07:26:28 -0500

Seen: 426 times

Last updated: Oct 06 '17