B в базовой системы координат имеет следующий вид:
(16)
где – вектор положения центра масс соединительного звена от точки В в базовой системы координат;
– ускорение центра масс соединительного звена.
В выражение (16) входит IB – тензор инерции соединительного звена в точке B.
При этом направление осей берется параллельно осям базовой системы координат. Компоненты тензора инерции в этом случае являются переменными величинами, зависящими от положения соединительного звена, что значительно усложняет решение задачи. Наоборот, тензор инерции соединительного звена в начале системы координат BXcYcZc, неизменно связанной с соединительным звеном, является заданной массово-инерционной характеристикой соединительного звена. Указанное обстоятельство послужило основной причиной того, что расчеты в дальнейшем ведутся в локальной системе координат BXcYcZc. При этом тензор инерции соединительного звена в локальной системе координат характеризуется матрицей
![](data:image/png;base64,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) , (17)
где – осевые моменты инерции соединительного звена относительно осей координат системы BXcYcZc;
Достарыңызбен бөлісу: |