Geometrical Anatomy Index Page

Geometrical Anatomy

Manifesto what is new and significant about these studies Quaternion Analysis theoretical papers Links other websites related to quaternions and anatomy Eye Movements the description of eye movements and muscle pulls Dr. Langers's Website a link to departmental website: Anatomy and Cell Biology University of Saskatchewan Atlanto-Axial Joint movements of the atlanto-axial joint and implications for vertebral artery flow Description of Strain Using quaternions to describe strain Lower Cervical Spine The anatomy of the lower cervical vertebrae and how they move Books on Quaternions Quaternions and Anatomical Movements A book that summarizes this work Compound Movements   Movement in multijointed systems Equivalent Descriptions of Movements Conversion between descriptions of complex rotations Angular Momentum An analysis of angular momentum in terms of quaternions Anatomy and Function of Semicircular Canals Consideration of the implications of the anatomy of the semicircular canals

Manifesto  |  Links  |  Dr. Langers's Website  |  Strain Quaternion Analysis  |  Eye Movements  |  Cervical Spine  | Compound Movt's |  Lumbar Spine Equivalent Descriptions | Angular Momentum | Semicircular Canals

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Quaternions and Anatomical Movements
{A book that introduces the basic concepts with applications}

Table of Contents [Word | PDF]
Title Page [Word | PDF]
Preface [Word | PDF]
Introduction to Quaternions and Anatomical Movements [Word | PDF]
An Intuitive Logical Formalism for the Description of Anatomical Movements [Word | PDF]
Transformation of Orientation: Revisiting Spin and Swing [Word | PDF]
Transformations of Orientation in a Universal Joint [Word | PDF]
Spinal Dynamics I: The Axio-atlanto-occipital Assemblage [Word | PDF]
Spinal Dynamics II: Lower Cervical Spine Anatomy [Word | PDF]
Spinal Dynamics III: Computing Compound Movements [Word | PDF]
Spinal Dynamics IV: Applying the Model to the Lower Cervical Spine [Word | PDF]
Spinal Dynamics V: Another Oblique Rotation [Word | PDF]
On Evolutes and Frames of Curves [Word | PDF]
Distorting the Box: Strain in Anatomical Media [Word | PDF]
Bubble Strain: The Measurement of Shear by the Distortion of Spheres [Word | PDF]
Orthogonalized Strained Boxes [Word | PDF]
Distortions in Media: Compressive and Tensile Strain [Word | PDF]
Distortions in Media: Shear Strain [Word | PDF]
Quaternion Numbers [Word | PDF]
Final Thoughts on the Control of Placement in Anatomical Systems [Word | PDF]

Quaternion Analysis: papers primarily concerned with theory

• Geometrical Anatomy  [ Word | PDF]
• Introduction to Quaternion Analysis   [ Word | PDF]
• Introduction to Quaternions   [ Word | PDF]
• Commentary on Joly   [ Word | PDF]
• Structural Ratios   [ Word | PDF]
• Compound Movements   [ Word | PDF]
• Catastrophes: abutment and tethering   [ Word | PDF]
• On Ligaments   [ Word | PDF]
• Quaternion Shear   [ Word | PDF]

Eye Movements

• Analysis of a Universal Joint: Movements and Muscles of the Eye   [ Word | PDF]
• Geometrical Anatomy of the Eye and Eye Movements: A Model with Restricted Extraocular Muscles   [ Word | PDF]
• Spin Neutrality and Eye Movement Trajectories   [ Word | PDF]

Cervical Spine

Upper Cervical Spine

• Brief Summaries of the Essays   [ Word | PDF]
• A Model of the Upper Cervical Assembly   [ Word | PDF]
• Response to Position   [ Word | PDF]
• Response to Differences in Technique   [ Word | PDF]
• Waveform Analysis   [ Word | PDF]
• Vertebral Artery Strain   [ Word | PDF]
• Flow in a Strained Vertebral Artery   [ Word | PDF]
• Why Sideflexion? The Role of the Alar Ligament   [ Word | PDF]

Lower Cervical Spine

• Building a Neck  [ Word | PDF]
• Lower Cervical Spine Model   [ Word | PDF]
• Movements in Artificial Necks   [ Word | PDF]
• Centers of Rotation in the Cervical Spine   [ Word | PDF]
• Disc Strains. Why do we not have lumbar discs in our neck?   [ Word | PDF]

Description of Strain

Analysis of Strain   [ Word | PDF]
Compression Between Parallel Plates   [ Word | PDF]
Point and Linear Depressions   [ Word | PDF]
The Diagonal Vector   [ Word | PDF]
Properties of a Distorted Box   [ Word | PDF]
Extension and Orientation Strain   [ Word | PDF]
Determining the Ellipse That Fits Three Vectors   [ Word | PDF]
Shear   [ Word | PDF]
Shear Displacement Between Parallel Plates   [ Word | PDF]
Finding the Transformation of a Cubic Box: the orientation of strained boxes   [ Word | PDF]
Torsional Strain   [ Word | PDF]
Strained Boxes and Products of Three Vectors   [ Word | PDF]

Equivalent Descriptions of Movements

Constructing Equivalent Descriptions of a Rotation   [ Word | PDF]
Parsing Movement Descriptions: Equivalent Movements   [ Word | PDF]

Compound Movements

Anatomical Descriptions That Compute Functional Attributes   [ Word | PDF]
Compound Movements in Multi-joint Systems   [ Word | PDF]
The Anatomical Geometry of Muscles Sets   [ Word | PDF]
Muscle Set Surfaces as a Function of Joint Anatomy   [ Word | PDF]
Snakes, Swan’s Necks, and Puppy Dog Tails   [ Word | PDF]
How Ligaments Restrict Movement   [ Word | PDF]

Angular Momentum

Quaternion Analysis of Momenta and Forces Acting Upon a Rigid Body   [ Word | PDF]

Anatomy and Function of the Semicircular Canals

The Functional Anatomy of the Semicircular Canals in Man   [ Word | PDF]
Movements of a Circular Canal   [ Word | PDF]

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