Theoretical Morphology of Fossil Cephalopods: Geometry and Hydrostatics of Compressed and Depressed Shells

头足类理论形态涉及平面螺旋壳几何的数学表征。这种分析有助于促进对头足类化石适应和进化的研究，特别是在与活体动物的静水特性有关的问题上。然而，这种方法受到限制，因为它只适用于具有圆形螺纹截面的壳体。这项建议中描述的研究将通过建立方程来生成压缩和凹壳的曲线面积和其他关键几何参数，从而消除这一缺点。此外，这项工作还将纠正古生物学家用来评估头足类化石稳定性和方向性的方法的不一致之处。新的程序将被用来评估壳体几何形状的变化对浮力、取向和静水稳定性的影响，所涉及的壳体形状范围比过去要大得多。目的是确定壳体的压缩和凹陷如何影响壳体的静水力学性能。这项工作的结果将极大地提高对头足类化石生活习性和古生态学的认识，并将使在水动力学、运动学和其他头足类适应和进化领域的迫切需要的工作成为可能。

Cephalopod theoretical morphology involves mathematical characterization of planispiral shell geometry. Such analysis has been instrumental in facilitating research on fossil cephalpood adaptation and evolution, particularly in matters relating to the hydrostatic properties of the living animals. However, this approach is handicapped by its strict applicability only to shells with circular whorl cross sections. The research described in this proposal will remove this shortcoming by developing equations for generating curve area and other key geometric parameters of compressed and depressed shells. In addition, this work will correct inconsistencies in the methods used by paleontologists to evaluate stability and orientation of fossil cephalopods. The new procedures will then be used to evaluate the effects of variation in shell geometry on buoyancy, orientation, and hydrostatic stability over a much wider range of shell form than could be achieved in the past. The objective is to determine how shell compression and depression influence hydrostatic properties of the shell. The results of this work will substantially improve knowledge of fossil cephalopod life habits and paleoecology, and will make possible much needed work in hydrodynamics, locomotion, and other areas of cephalopod adaptation and evolution.