3D Dynamics - Vibrations for aircrafts

Blogs

October 15, 2026

Tl;DR

The moment 2D mechanics is not enough.

Intro

WHY Im writting this post: Bc I want to fully understand all 3d effects that will affect me during my ULM/PPL prep and as a way to test my mbsd oss fwk
What Ive learnt with it: Ive ended

The dimension reduction worked great for cars.

But how about airplanes?

Can we use 2D or 3D is a must?

3D Dynamics x Airplanes

While 2D is the “speed king” for automotive refinement, the airplane use case is where the Dimensional Reduction Lemma finally hits a hard wall.

In an aircraft, you aren’t just sitting on a chassis that moves up and down; you are strapped to a power plant that is physically trying to twist the entire airframe.

For an airplane, 3D is a must for three primary reasons:

The Gyroscopic Precession (The “Cross-Axis” Moment)

A spinning propeller and crankshaft act as a giant gyroscope.

In a car, the chassis stays relatively level.

In a plane, you are constantly pitching (climbing/diving) and yawing (turning).

The Physics: If you have a massive propeller spinning at 2500 RPM and you suddenly kick the rudder to yaw the plane left, the gyroscopic effect generates a massive pitch moment that tries to pull the nose up or down.
The Solver Requirement: This is a cross-product effect ($\vec{M} = \vec{\omega} \times \vec{L}$).

⚠️

Since it couples the rotation of one axis to a moment in another, it cannot be modeled in a single 2D plane

Thrust-Moment Coupling

In our 2D engine model, we focused on “shake” (inertial forces). In an airplane, the Thrust is a massive constant vector acting along the $z$-axis (the one we ignored in 2D).

The Offset: If the engine is mounted even slightly above or below the center of gravity of the wing or fuselage, that thrust creates a permanent pitching moment.
Engine Mounts: Airplane mounts (often called “Lord mounts”) have to handle this constant axial tension/compression while still isolating the $1\times$ and $2\times$ vibration from the cockpit. A 2D model literally cannot see the $z$-axis thrust.

Six-Degree-of-Freedom (6-DOF) Airframe Response

In a car, “Ground” is a stiff, heavy chassis.

In a plane, the “Chassis” is a lightweight, flexible aluminum or carbon fiber tube.

Complex Transmissibility: An engine vibration might start as a vertical shake at the nose, but because the fuselage is long and flexible, it might manifest as a tail-wagging vibration at the rear.
The Mount Matrix: Airplane mounts are often arranged in a “ring” or “dynafocal” configuration, where the mounts are angled so their focal point is the engine’s CG. This makes the $K$ (stiffness) matrix a dense 6×6 block that couples every single translation to a rotation.

Feature	2D Multi-Body	3D Multi-Body
Piston Inertia	Perfect	Same
Combustion Force	Perfect	Same
Propeller Thrust	Hidden	Visible
Propeller Gyroscopics	Impossible	Required
Tail-Wagging (Yaw)	Impossible	Required

If you are designing the internal balance of the engine (e.g., “Do I need counterweights on this Lycoming O-360 crankshaft?”), the 2D phasor framework is still the best and fastest tool.

But the moment you want to know “Will the pilot feel a vibration in the rudder pedals during a steep turn?”, you have to leave the 2D world and embrace the full 6-DOF 3D dynamics.

MBSD 0-9-0 Simulation

Coming from the 0-8-0 release, its time for the 0-9-0 where we take a good foundation around quaternons

scp jalcocert@192.168.1.2:/home/jalcocert/multibody-tests/v-0-8-1-concerns.md .

I got inspired by this project’s roadmap: https://dbackup.app/roadmap/ In fact, thats sth i want to have in my project soon, with a /changelog as well that feeds from the same the repo has.

No open fatigue around here.

For the 0-9-0 was like 🚀

#http://192.168.1.2:3034/hermesagent/mbsd/src/branch/oss-core-2d/web
cd /home/jalcocert/Desktop/mbsd-framework/mbsd-core

git switch main
git merge --ff-only v0.8.0-dev
git tag -a v0.8.0 -m "MBSD Core v0.8.0"
git push origin main
git push origin v0.8.0

awk '
  /^## v0\.8\.0 / { found=1; next }
  /^## / && found { exit }
  found { print }
' CHANGELOG.md | gh release create v0.8.0 \
  --repo JAlcocerT/mbsd-core \
  --verify-tag \
  --title "MBSD Core v0.8.0 - Constrained spatial kinematics" \
  --notes-file - \
  --latest

Then examples:

cd /home/jalcocert/Desktop/mbsd-framework/mbsd-examples

git switch main
git merge --ff-only v0.8.0-dev
git tag -a v0.8.0 -m "MBSD Examples v0.8.0"
git push origin main
git push origin v0.8.0

awk '
  /^## v0\.8\.0 / { found=1; next }
  /^## / && found { exit }
  found { print }
' CHANGELOG.md | gh release create v0.8.0 \
  --repo JAlcocerT/mbsd-examples \
  --verify-tag \
  --title "MBSD Examples v0.8.0 - Constrained spatial kinematics" \
  --notes-file - \
  --latest

The remaining roadmap:

fixed-orientation constrained translational dynamics

0.9.0: real rotational dynamics and orientation integration.
0.9.1: rotational joints, forces and torques.
0.9.2: 2D/3D API symmetry, documentation and API freeze.
1.0.0: stable minimal 2D/3D kinematics and dynamics.

v0.8.1 contains no dynamics. All four v0.8.0 concerns are now addressed:

Contradictory drive value/velocity laws are rejected.
Trajectory diagnostics compare pose derivatives with reported linear and angular velocities.
model_id identifies structure; excitation_id identifies sampled drive behavior.
Highly underconstrained systems use rank-aware minimum-norm projection.
Nested result validation remains fully hardened.

Verification:

Core: 95 tests passed.
Examples: 28 tests plus all runnable examples passed.
Ruff, builds, Twine and isolated wheel smoke tests passed.
Both dev branches are clean.

Latest commits:

Core: 3c81df0
Examples: 7a4c19c

And yes: the former 0.8.2 dynamics preview belongs in 0.9.0. After releasing 0.8.1, we should create a fresh v0.9.0-dev from it and selectively bring over the useful old dynamics work rather than releasing v0.8.2-dev.

All six findings are addressed on v0.8.1-dev.