When it comes to finding synonyms for the phrase "study at battle," there are several options to choose from. One possible alternative is "investigate conflict," which implies a focus on finding the root causes of the disagreement or dispute. Another option is "analyze combat," which suggests a more detailed examination of the specific tactics and strategies used by opposing forces. "Scrutinize struggle," on the other hand, brings attention to the effort and determination required to overcome obstacles during a war or conflict. Overall, there are many ways to describe the act of studying or researching warfare, and the specific choice of words will depend on the subject matter and context.