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1-1 Find the angular velocity Gv(t) by using GRB (t) Br

1-1 Find the angular velocity Gv(t) by using GRB (t) Br

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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**Problem 1.1**: Find the angular velocity \( Gv(t) \) by using \( G\dot{R}_B(t) \, \mathbf{r}^B \). This task involves calculating the angular velocity, designated as \( Gv(t) \), utilizing the derivative of \( G R_B(t) \) and the vector \( \mathbf{r}^B \). The notation suggests that a rotational matrix \( G R_B(t) \) is differentiated with respect to time, contributing to the understanding of angular motion in a specific frame. **Instructions for Students**: Derive \( Gv(t) \) by applying the appropriate mathematical operations on \( G\dot{R}_B(t) \) and consider how \( \mathbf{r}^B \) impacts the angular velocity through its positional vector.
Transcribed Image Text:**Problem 1.1**: Find the angular velocity \( Gv(t) \) by using \( G\dot{R}_B(t) \, \mathbf{r}^B \). This task involves calculating the angular velocity, designated as \( Gv(t) \), utilizing the derivative of \( G R_B(t) \) and the vector \( \mathbf{r}^B \). The notation suggests that a rotational matrix \( G R_B(t) \) is differentiated with respect to time, contributing to the understanding of angular motion in a specific frame. **Instructions for Students**: Derive \( Gv(t) \) by applying the appropriate mathematical operations on \( G\dot{R}_B(t) \) and consider how \( \mathbf{r}^B \) impacts the angular velocity through its positional vector.
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