Вот так изучаешь английский язык последние 28 лет, и вдруг попадается совершенно незнакомая тема в грамматике –
https://en.wikipedia.org/wiki/Exceptional_case-marking
https://en.wikipedia.org/wiki/Accusative_and_infinitive
I have never heard you sing.
I heard her come up the steps.
I saw her run into the house.
What I would like is for things to get better.
She had me cook, or at least try to.
She had my watch fixed.
Being in America 