行星轨道模拟2a:多体运动与几何构造
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该范例演示了围绕多个行星的轨道运动,通过动态几何方式展示天体运行轨迹与相关几何关系。核心数学概念包括圆、圆锥曲线、坐标几何、向量平移以及减法运算,同时涉及分布与二项分布等统计元素,但主体仍是几何构造与运动模拟。作图要点:使用GeoGebra命令如Point、Segment、Polygon、Slope、Circle、Area、PointIn、Line、Intersect、Name、Midpoint、Vector、Translate等,构建了多个点、线段、多边形、圆及向量对象,并通过滑块或参数控制轨道变化。适合中学数学或物理课程中用于演示行星运动、几何变换与坐标关系,也可用于探索圆锥曲线与统计分布的交叉应用。
GeoGebra 命令及参数
Point(b) → APoint(c) → BSegment(C, A) → dSegment(C, B) → fPoint(c) → DSegment(B, D) → iPoint(Circle[A, 1.4142135623730951]) → FSegment(A, F) → gSegment(A, F) → hPolygon(B, C, D) → poly1, d_1, b_1, c_1Segment(C, D) → d_hPoint(c) → EPoint(c) → GSegment(B, G) → τSegment(F, G) → nSlope(n) → mSlope(d_h) → m_1Circle(C, A) → kArea(k) → ePointIn(k) → PointkLine(H, f) → jIntersect(k, j, 2) → ISegment(C, I) → lLine(I, b) → pIntersect(p, d) → JSegment(C, J) → qSegment(J, I) → sPoint(s) → KSegment(C, K) → tSegment(I, F) → a_1Segment(J, A) → e_1Polygon(C, I, F, G, B) → poly2, c_2, i_1, f_1, g_1, b_2Name(o) → A1Name(u) → B1Name(a) → C1Point(k) → LCircle(M, N) → h_1Point(h_1) → OPoint(h_1) → PMidpoint(O, P) → QSegment(M, O) → j_1Segment(z_1, z_2) → k_1Vector(T, U) → vTranslate(z_1, v) → z_3Translate(z_2, v) → z_4Segment(z_3, z_4) → l_1Point(l_1) → VSegment(V, W) → n_1Segment(V, Z) → p_1Segment(V, A_1) → q_1Segment(V, B_1) → r_1Segment(V, C_1) → s_1Segment(V, D_1) → t_1Segment(V, E_1) → a_2Segment(V, F_1) → d_2Segment(V, G_1) → e_2Point(j_1) → H_1Circle(H_1, I_1) → f_2Circle(H_1, J_1) → g_2Circle(H_1, K_1) → h_2Circle(H_1, L_1) → k_2Circle(H_1, M_1) → p_2Circle(H_1, N_1) → q_2Circle(H_1, O_1) → r_2Point(h_1) → P_1Circle(H_1, P_1) → s_2Segment(V, Q_1) → i_2