Глагол "двигать" (причем в старом значении, как "дергать") уже видели?

дви́гать

дви́гаю, буд. дви́ну, сюда же подвиза́ться, укр. дви́гати, ст.-слав. двигнѫ, двигнѫти, движѫ, двиѕати, болг. ди́гам, сербохорв. ди̏гнути, ди̏ħи, словен. dvígati, dvîgam, чеш. zdvihnouti, польск. dźwigąć "поднять, возвести", в.-луж. zběhać, н.-луж. zwigaś.

Неясно. Возможно сопоставление с англос. twiccian "рвать, дергать" , англ. twitch (Эндзелин, ЖМНП, 1910, июль, стр. 201).

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Разбор этимологии выражения "I am" от "Аз есмь":

//am (v.) Look up am at Dictionary.com
Old English eom "to be, to remain," (Mercian eam, Northumbrian am), from PIE * esmi - (source also of Old Norse emi, Gothic im, Hittite esmi, Old Church Slavonic jesmi, Lithuanian esmi), from root *es-, the S-ROOT, which also yielded Greek esti-, Latin est, Sanskrit as-, and German ist.

In Old English it existed only in present tense, all other forms being expressed in the W-BASE (see were, was). This cooperative verb is sometimes referred to by linguists as *es-*wes-. Until the distinction broke down 13c., *es-*wes- tended to express "existence," with beon meaning something closer to "come to be" (see be).

Old English am had two plural forms: 1. sind/sindon, sie and 2. earon/aron. The s- form (also used in the subjunctive) fell from use in English in the early 13c. (though it continues in German sind, the 3rd person plural of "to be") and was replaced by forms of be, but aron (aren, arn, are, from Proto-Germanic *ar-, probably a variant of PIE root *es-) continued, and as am and be merged it encroached on some uses that previously had belonged to be. By the early 1500s it had established its place in standard English. Art became archaic in the 1800s.//

http://www.etymonline.com/index.php?l=a&p=23&allowed_in_frame=0