The Stability of Cylindrical Pendant Drops.
- 1st ed.
- 1 online resource (122 pages)
- Memoirs of the American Mathematical Society ; v.250 .
- Memoirs of the American Mathematical Society .
Cover -- Title page -- Introduction -- Chapter 1. Normalization, stability condition, and elementary properties -- 1.1. ODEs for Cylindrical Profiles -- 1.2. Elementary Properties -- 1.3. Proofs of Elementary Properties -- Chapter 2. One Parameter Families -- Definition of ₂ -- 2.1. Continuous families -- 2.2. Enclosed volume/cross-sectional area -- 2.3. Smooth families -- profile arclength -- 2.4. More on enclosed volume -- 2.5. Further properties of drop profiles -- Chapter 3. Stability -- 3.1. Separation of Variables -- 3.2. Decomposition -- 3.3. Secondary variational problems and PDE results -- 3.4. Initial Stability -- 3.5. Geometric interpretation of (H) -- 3.6. Geometric interpretation of (V) -- initial stable families -- 3.7. A surprise -- Chapter 4. Infinitely long drops -- Chapter 5. Zero gravity and soap bubbles -- Chapter 6. Open problems -- Appendix 1: Explicit formulas -- Appendix 2: Sturm-Liouville Theory -- Appendix 3: Elliptic integrals -- Acknowledgement -- Bibliography -- Back Cover.
The author considers the stability of certain liquid drops in a gravity field satisfying a mixed boundary condition. He also considers as special cases portions of cylinders that model either the zero gravity case or soap films with the same kind of boundary behavior.