Evolution of Cholesky factor given evolution of symmetric positive definite matrix

Question

Given that the matrix $A$ is symmetric positive definite, and governed by the following set of ODEs for some matrix $B$:

$$\frac{dA}{dt}+AB+B^TA=0$$

is is possible to derive an evolution equation for the Cholesky factor $L$ where $A=LL^T$?

Answer 1

$$\frac{dA}{dt} = \frac{dLL^\top}{dt} = L\frac{dL^\top}{dt} + \frac{dL}{dt}L^\top.$$