The three pages define and explain the components of the Generalized Inertia Tensor matrix $\mathbf{M}$ for a coupled mass system using generalized coordinates $r$ and $\phi$. The final form of the matrix is diagonal, $\mathbf{M} = \begin{pmatrix} m_1 + m_2 & 0 \\ 0 & m_1 r^2 \end{pmatrix}$, which explicitly shows that the radial and angular motions are inertially uncoupled. Specifically, the radial inertia component $M_{rr}$ is the total mass ($m_1 + m_2$) because both masses move with the radial speed $\dot{r}$, and the angular inertia component $M_{\phi\phi}$ is the moment of inertia ($m_1 r^2$) of mass $m_1$ alone, as only the mass on the horizontal plane contributes to the rotation.
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