Howell - math of Lucas Universal Force, verifications summary listing 07Jan2016 11h59m11s.txt As of : Thu Jan 7 11:59:11 2016 Only the first line of the comments is provided - many equations have long explanations in "Howell - math of Lucas Universal Force.ndf". 04_01 NYET - I have to check Appendix A later... 04_02 important ?error? is the reversal of the integration/derivative operators!! 04_03 Overall - reasonable, but may have glitches 04_04 OK - piece of cake... 04_05 Can't seem to find support for this specific form 04_05a Didn't look for this yet, but Jackson shows "Normal" linear superposition, except solid materials, extreme conditions. 04_06 WRONG - Lucas 4-06 versus 4-26, missing q*vB(r,v,t), still the 1/c problem! 04_07 This is straightforward, so I wont check. (eg Jackson 1999 p515h0.55 Eq (11.1) 04_08 CHANGED - Must check Appendix A Equation (A19), I put Ei, not E0? 04_09 CLOSE Lucas versus Jackson - problem with [c,μ0,ε0,4,π], d^3r 04_10 repeat statement - no need to re-check 04_11 critical distinction between static & induced - have to check later 04_12 KEY POINT - need to research results and opinions, seems correct 04_13 OK - except I think Lucas should NOT have the i subscript with Bi(r,v,t) 04_14 CLOSE - missing c (check Jackson), depends on (4-1) check, problem with [c,μ0,ε0,4,π] 04_14a OK, simple, but just use rhp = rp/|rp|? 04_15rev1 PRIORITY WRONG : I have *rs/|r - v*t| in 2nd term, B not Bi 04_16rev2 Wait IN PROGRESS : - it works! but I use Op not Oo 04_17rev2 02Jan2016 OK - easy 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_20 OK - straight defn. Usage explained by Jackson (to generalize Faradays Law?) 04_21 OK - works great 04_22 didn't do - I don't see the point of deriving (4-22) !?! 04_23 OK - seems good 04_24 !!!WRONG - On hold as I haven't been able to "move" (v/c) to the right place.. 04_25 OK - straightforward from (4-24) 04_26 OK - very straightforward 04_27 OK - but Im still unsure that I've properly defined ∇p 04_28arev1 OK - straightforward. 04_28brev1 OK - Simple! I used (4-16). 04_29arev1 !!!WRONG - I'm lost right now... 04_29brev1 INCOMPLETE - need to redo this! ... but not a high priority 04_30rev4 OK - simple. 04_31 ???Hmm - something is wrong here. havent done yet. 04_31a Machs principle - Important issue for Lucas. not done yet. I"ll have to think this over... 04_32rev3 WRONG - I have (b*rs)^2 rather than b*rs, Ei,E0 rather than Eis,E0s 04_33rev1 OK - works great by using a blend of Lucas & Howell expressions 04_34rev3 WRONG - I have r^2&r^0 in the middle terms, not r^4&r^2 04_35rev3 OK - I have Op rather than Oo, Ei(rs,vs) not E(r) 04_36 OK - very simple! assuming it is for Ei(rs), NOT E(rs)?? 04_37rev10 PRIORITY to address!!! 03Jan2016 04_38 OK - simple 04_39 OK - simple 04_40 no need to do - from Jackson1999, standard formula 04_41 PRIORITY PROBLEM - sin,cos terms 04_42 havent done yet 04_43 OK - simple BUT EO -> B issue? 04_44 OK - works, except |E0(r)|, which makes sense, but I missed? 04_45 OK - not required as follows directly from (4-46) 04_46 OK - very simple 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 ??_list end_?? havent done yet