Statics & Structures
Center of Gravity Simulator
Examine center of gravity / barycenter shifts in a 2D particle system. Modify coordinates and masses of three individual nodes, or run a sweep animation.
Total Mass
45.0 kg
3 loaded nodes
Centroid
(5.33, 4.67)
Geometric CoG
Output
CSV
Export ready
Parameters
Preset Layout
Configure Node
Node 1 X-sweep
System Governing Equations
Centroid X-Coordinate
X̄ = (m1·x1 + m2·x2 + m3·x3) / Σmi
Centroid Y-Coordinate
Ȳ = (m1·y1 + m2·y2 + m3·y3) / Σmi
The centroid or Center of Gravity represents the weighted mean position of the system's mass.
If the masses are equal, the CoG simplifies to the geometric centroid of the triangle vertex points.
Linked System Geometry
Centroid X (X̄)
5.33m
Centroid Y (Ȳ)
4.67m
Node 1 Contribution
22.2%
Total Mass
45.0kg
Centroid Shift vs Mass 1
Mass Variation Matrix
| Mass 1 (kg) | Centroid X (m) | Centroid Y (m) |
|---|---|---|
| 1 kg | 6.17 m | 5.33 m |
| 9 kg | 5.41 m | 4.73 m |
| 17 kg | 4.88 m | 4.31 m |
| 25 kg | 4.50 m | 4.00 m |
| 33 kg | 4.21 m | 3.77 m |
| 41 kg | 3.97 m | 3.58 m |
| 49 kg | 3.79 m | 3.43 m |