摘要
火箭(或导弹)所受空气动力必在总攻角平面的结论,是利用总攻角分析零攻角再入、以配平攻角飞行等典型的再入段运动的基础,但在现行弹道轨道动力学的教材中,往往不加证明地给出这一并不显然的结论,在教学中容易引起学生的困惑,也不利于学生掌握这一结论。针对这一问题,综合应用速度坐标系与箭体坐标系的变换关系、火箭气动系数的对称关系以及小角度三角函数的近似计算,给出了该结论的两种证法与分析,指出这个结论的证明依赖于火箭气动系数的对称关系,可以推广至返回与再入段的弹头或返回舱。证明过程的综合性较强,可帮助学生对前期所学知识融会贯通,同时这一证明也是运用纯数学工具解决工科专业问题的典型范例,有助于培养工科学生的应用数学思维,提高学生的数学建模能力。
The conclusion that the aerodynamic force of the rocket (or missile) must be in the plane of total angle of attack is often given without proof in the current textbook of ballistic trajectory dynamics, but this is not an obvious conclusion, which is easy to cause students’ confusion in teaching. To solve this problem, two proofs and analysis of this conclusion are given by comprehensively applying the transformation relationship between the velocity coordinate system and the body coordinate system, the symmetry relationship of the rocket aerodynamic coefficient and the approximate calculation of trigonometric functions with the small angle. It is pointed out that the proof of this conclusion depends on the symmetry relationship of the rocket aerodynamic coefficient and can be extended to the warhead or return capsule in the return and reentry phase. The proof process is highly comprehensive and is very suitable to be explained as a typical example, which is helpful for students to master the previous knowledge. At the same time, this proof is also a typical example of using pure mathematical tools to solve engineering problems, which is helpful to cultivate engineering students’ applied mathematical thinking and improve students’ mathematical modeling ability.
出处
《教育进展》
2022年第6期1955-1962,共8页
Advances in Education
