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One of the important tools of geometric mechanics is reduction theory (either Lagrangian or Hamiltonian),which provides a well-developed method for dealing with dynamic constraints. In this theory the dynamic constraints and the sym- metry group are used to lower the dimension of the system by constructing an associated reduced system. We develop the Lagrangian version of this theory for nonholonomic systems in this paper. We have focussed on Lagrangian systems because this is a convenient context for applications to control theory. . | CHAPTER 2 OCEANOGRAPHIC ELECTRO-MECHANICAL CABLES Albert G Berian Reviewed and edited 2000 by Len Onderdonk 1.0 CONSTRUCTION CHARACTERISTICS 2-5 1.1 Coincidence 2-5 1.2 Center Strength Member 2-5 1.3 Braided Outer Strength Member 2-5 1.4 Electro-Mechanical Wire Rope 2-5 1.5 Outer Single Served Strength Member 2-5 1.6 Outer Double Served Strength Member 2-5 1.7 3-4-5 Layer Served Strength Member 2-8 2.0 WORKING ENVIRONMENT 2-8 2.1 Flexing 2-8 2.2 Abrasion 2-9 2.3 Te nsion Cycling 2-9 2.4 Corrosion 2-9 2.5 Fish Bite 2-10 2.6 Abrasion Rate Factors 2-10 2.7 Kinking 2-10 2.8 Crushing 2-11 3.0 PARTS OF CONTRA-HELICALLYARMORED 2-11 EM CABLE 3.1 Direction of Lay 2-11 3.2 Lay Angle 2-12 3.3 Preform 2-12 3.4 Height of Helix 2-13 3.5 Percent Preform 2-13 3.6 Length of Lay 2-13 3.7 Pitch Diameter 2-14 3.8 Number of Armor Wires 2-14 3.9 Armor Coverage 2-16 3.10 Squeeze 2-16 3.11 Core 2-17 3.12 Water Blocked Core 2-18 2-2 4.0 PERFORMANCE CHARACTERSITICS OF 2-19 C-H-A E-M CABLES 4.1 Torque Balance 2-19 4.2 TwiSt Balance 2-21 4.3 Crush Resistance 2-21 4.4 Corrosion Resistance 2-22 4.5 Abrasion Resistance 2-24 4.6 Elongation 2-24 4.7 Sea WaterBuoyancy 2-24 4.8 Breaking Strength 2-24 5.0 MANUFACTURING PROCESSES FOR E-M 2-27 CABLES 5.1 Conductor Stranding 2-27 5.2 Insulation 2-27 5.3 Wet Test 2-28 5.4 Cabling 2-28 5.5 Braiding 2-28 5.6 Serving 2-28 5.7 Jacketing 2-29 5.8 Armoring 2-29 5.9 Prestressing 2-30 6.0 HANDLING E-M CABLES 2-33 6.1 Storage Before Use 2-33 6.2 Spooling Effect on E-M Cables 2-34 6.3 Smooth Drum Spooling 2-35 6.4 Tension Spooling Objectives 2-35 6.5 Tensions for Spooling 2-35 6.6 Lower Spooling Tensions 2-37 6.7 Grooved Drum Sleeves 2-37 6.8 Sheaves 2-37 7.0 FIELD INSPECTION AND TESTING 2-42 7.1 Ge neral 2-42 7.2 Required Inspections 2-42 7.3 Cable Record Book 2-42 7.4 Cable Log 2-43 2-3 7.5 Inspection 2-43 7.6 Visual Inspection Practices 2-43 7.7 Armor Tightness Inspection 2-44 7.8 Lay Length of the OUter Armor 2-46 7.9 Conductor Electrical Resistance 2-47 7.10