Rigid Body Rotation

Loading the math board and drawing, please wait…

2016-04-28 07:56

Vector Matrix

This example demonstrates the geometric phenomenon of rigid body rotation. Key mathematical concepts include rotation matrices and vectors. Using GeoGebra commands such as Sequence, Circle, and Line, the dynamic transformation of a rigid body during rotation is illustrated. Suitable for high school and above students to learn about geometric transformations and vectors.

GeoGebra Commands & Parameters

Sequence(Sequence[Vector[(j, k), (j + (scale * F_1(j, k)), k + (scale * F_2(j, k)))], j, xmin, xmax, xstep], k, ymin, ymax, ystep) → vField
Sequence(((x(Element[inicialPts, i]) * cos((w * time))) - (y(Element[inicialPts, i]) * sin((w * time))), (x(Element[inicialPts, i]) * sin((w * time))) + (y(Element[inicialPts, i]) * cos((w * time)))), i, 1, 8) → particlesList
Sequence(CurveCartesian[(x(Element[inicialPts, i]) * cos((w * t))) - (y(Element[inicialPts, i]) * sin((w * t))), (x(Element[inicialPts, i]) * sin((w * t))) + (y(Element[inicialPts, i]) * cos((w * t))), t, 0, time], i, 1, 8) → pathlinesList
Sequence(Vector[Element[particlesList, i], (x(Element[particlesList, i]) + (scale * F_1(x(Element[particlesList, i]), y(Element[particlesList, i]))), y(Element[particlesList, i]) + (scale * F_2(x(Element[particlesList, i]), y(Element[particlesList, i]))))], i, 1, 8) → vectorParticles
Sequence(Segment[Rotate[curlPt - (0.6, 0), k + curlAngle, curlPt], Rotate[curlPt + (0.6, 0), k + curlAngle, curlPt]], k, 0, 2.0944, 1.0472) → spokes
Circle(divPt, 0.6) → divGlowCircle
Line(I, xAxis) → f
Line(J, xAxis) → g
Line(K, xAxis) → h