加速度合成定理的几何法证明

摘要

For acceleration composition theorem, when the carrier motion is general, to sho w the mechanical cause of Coriolis′ acceleration, based on the original concept of acceleration, expression aａ＝lim Δt→0Δv aΔt and velocity composition theorem v a＝vｅ＋vｒ， acceleration composition theorem is deduced by geometrical method. This metho d can clearly show the mechanical cause of Coriolis′ acceleration.The relative ve lo city direction being changed by carrier motion and the position of carrier point being changed by relative motion, two items of additional acceleration are gene rated, and each part has the same expression as ω ×vｒ， so the expression of Coriolis′ acceler ation is aC＝2ω×vｒ .%为了直观地给出牵连运动为一般运动时加速度合成定理中科氏加速度产生的力学原因，从 加速度的原始定义出发，据表达式aａ＝lim Δt→0Δv aΔt，并利用速度合成定理vａ ＝vｅ＋vｒ，用几何 法推导出牵连运动为一般运动时点的加速度合成定理，这种证明方法下，科式加速度产生的 力学原因明确。即：由于牵连运动改变了相对速度的方向及由于相对运动改变了牵连点的位 置，因而有两部分附加加速度产生，每一部分的表达式均为ω × vｒ，从而科式加速度的表达式为aC＝2ω×vｒ 。