Problem 1.185

The angular momentum of a particle relative to a certain point $O$ varies with time as $\mathbf{M}=\mathbf{a}+\mathbf{b} t^{2},$ where $\mathbf{a}$ and $\mathbf{b}$ are constant vectors, with $a \perp b$. Find the force moment $N$ relative to the point $O$ acting on the particle when the angle between the vectors $\mathbf{N}$ and M equals $45^{\circ}$.