Howell - math of Lucas Universal Force, verifications by class of results.txt Results by class for verifications of Lucas' Chapter 4 equations. As of : Mon May 30 12:56:08 2016 WARNING : where I suggest Lucas has made an error - it is more likely that I have goofed! Also - I have used an early version of Lucas's book, for which many errors have already been corrected. I have NOT seen more recent versions, so my results will also show any weaknesses where I have missed errors. Older versions of derivations are in the file "Howell - Old math of Lucas Universal Force.ndf" - which is a record of my floundering. ******************* Likely_Lucas_error_or_omission 04_32rev4 29May2016 WRONG - (4-23) is for v=0, I have (b*rs)^2 rather than b*rs, and sinO instead of (cosO - 1) 04_34rev4 WRONG (Lucas&Howell) - maybe Lucas double-counted an "rs"?, his units DON'T balance. ******************* Lucas_Typo_or_omission 04_15rev3 09Jan2016 WRONG - I have Op rather than Oo in 2nd term. 04_28arev1 OK - straightforward, with a couple of concerns with Lucas's expression - reference frames & notational. 04_35rev3 OK other than reference frame mixup in Lucas's text, and this is for Ei, not ET as Lucas has it. ******************* Possible_Lucas_error_or_omission 04_16rev4Lucas4-15 09Jan2016 WRONG! : I use Op not Oo for 2nd term RHS (as with (4-15), different terms) 04_24 !!!WRONG - On hold as I haven't been able to "move" (v/c) to the right place.. ******************* Howell_error ******************* Problem_or_challenge 04_01 NOTE - I have to check Appendix A later... 04_02 OK - but DIFFERENT from Maxwell equation equivalent! : missing curl(E). Does this give good results for experimental data? 04_31 OK with concerns - Looks reasonable (see caveats below) and straightforward. No details needed here. ******************* need_further_support ******************* Howell_incomplete 04_31a Machs principle - Important issue for Lucas. not done yet. I"ll have to think this over... 04_37rev10 PRIORITY to address!!! 03Jan2016 04_41 PRIORITY PROBLEM - sin,cos terms 04_42 havent done yet ******************* Question 04_05 Qualitatively OK - but I can't seem to find support for this specific form. 04_13rev1 OK simple, but I have questions. 10Jan2016 04_18 Perfect - simple formula translation, BUT is Ep = E, as it looks 04_19 WRONG - Notice that I didnt have to apply Stokes theorem! 04_27rev1 OK - Note that this is for v=0 which seems inconsistent with "r - v*t", and I still unsure that I've properly defined ∇′ ******************* Re_check_later 04_17rev2 02Jan2016 OK - easy BUT, I still need to check angle basis below... 04_23 OK - seems good, Note that this is for v=0, but how is this different than (4-2) Faraday's Law? 04_30rev4 OK - simple, but possible problem with my reference frame mis-notations. ******************* no_issue 04_03 OK - same as conventional expression 04_04 OK - piece of cake... 04_05a I haven't looked for this yet, but Jackson shows "Normal" linear superposition, except solid materials, extreme conditions. 04_07rev1 OK - straightforward (eg Jackson 1999 p515h0.55 Eq (11.1) 04_08 OK - Must check derivation of Appendix A Equation (A19) 04_10 OK - repeat statement, no need to re-check 04_11 OK - but where is the effect of the critical distinction between static & induced - have to check later 04_12 OK, EASY - key point, I need to research results and opinions, seems correct 04_14a OK, simple, but just use rph = rpv/|rpv|? 04_20 OK - straight defn. Usage explained by Jackson (to generalize Faradays Law?) 04_21 OK - 2nd try gets same as Lucas 04_25 OK - straightforward from (4-24) 04_26 OK - very straightforward 04_28brev1 OK - Simple! I used (4-16). 29May2016 - still a concern => But - shouldn't all angles be primed to get particle/system refFrame? 04_29arev1 OK - straightforward, but clouded by some of the text explanations & omissions. 04_29brev1 OK - easy after fixing (4-29a) above 04_33rev1 OK - works great by using a blend of Lucas & Howell expressions for (4-32). 04_36 OK - very simple. 04_38 OK - simple 04_39 OK - simple 04_40 OK - no need to do asd it can be found from Jackson1999, standard formula 04_43 OK - simple, although I think primes are needed to denote particle reference frame (RFp) for angle theta (Op). 04_44rev1 OK - works, Problem - usage of angle Oo in observer reference frame (RFo) instead of Op in (RFp) 04_45 OK - not required as follows directly from (4-46) 04_46 OK - very simple, from textbooks 05_01 no need - same as Lucas04_44 05_02 havent done yet 05_03 havent done yet 05_04 havent done yet 05_05_pre havent done yet 05_07 havent done yet 05_08 havent done yet 05_09 havent done yet 05_10 havent done yet 05_11 havent done yet 05_12 havent done yet 05_13 havent done yet 05_14 havent done yet 05_15 havent done yet 05_16 havent done yet 05_17 havent done yet 05_18 havent done yet 05_19 havent done yet 06_01 no need same as Lucas05_04 06_02 no need - same as Lucas05_07 06_03 havent done yet 06_04 havent done yet 06_05 havent done yet 05_19 havent done yet 06_07 havent done yet 07_01 havent done yet 07_02 havent done yet 07_03 havent done yet 07_04 havent done yet 07_05 no need - same as Lucas05_07 07_06 havent done yet 07_07 havent done yet 07_08 havent done yet 07_Fig7_2 havent done yet 07_09 havent done yet 07_10 havent done yet 07_11 havent done yet 07_12 havent done yet 07_13 havent done yet 07_14 havent done yet 07_15 30Aug2015 Howell - I dont like this last step or two, but seems reasonable as result. 07_16 havent done yet 07_17 This looks wrong - improper integral 07_18 havent done yet 07_19 ERROR! should be as I have it 07_20 WRONG!! 07_21 I DONT LIKE THIS : He has simply stuck in more symbols 07_22 I DONT LIKE THIS : He has simply stuck in more symbols 07_23 Looks OK - going from (7-22) 07_24 ???OK - same number 07_25 havent done yet 07_26 havent done yet 07_27 havent done yet 07_28 WRONG expression in Lucas (7-28) : 07_29 havent done yet 08_01 havent done yet - but looks straightforward 08_02 havent done yet - but looks straightforward 08_03 havent done yet 08_04 havent done yet 08_05 havent done yet 08_06 havent done yet 08_F8_1 havent done yet 08_07 havent done yet 08_08 NOTE: key simplification! ignores surface effects locally, but may 08_09 havent done yet - Lucas ??NO square of |r2 - r1|? 08_10 havent done yet 08_11 ??Lucas said 8-8, but used 8-7, and used P1 not P?? 08_12 Used in (8-11) : This is the wrong integral?!? 08_13 havent done yet 08_14 havent done yet 08_15 havent done yet 08_16 havent done yet 08_17 havent done yet 08_18 Lucas07_25 := NOT APPLICABLE? - neutral dipoles, ?non-accelerating? 08_19 havent done yet 08_20 havent done yet 08_21 havent done yet 08_22 havent done yet 08_23 havent done yet 08_24 havent done yet 09_01 no need - same as (5-04) 09_02 no need - same as Lucas05_07 10_01 ???This doesnt make sense??? 10_02 NOTE : neutrons count too - perhaps he is using neutron = proton+electron 10_03 havent done yet 10_04 havent done yet 10_06 havent done yet 10_07 ?? Maybe not - each could balance??? 10_08 havent done yet 10_09 havent done yet 10_10 havent done yet 10_11 ?OK - constant orbital velocity of planets and moons in a solar system