"motivated us to" is correct and usable in written English. You can use it to describe how something motivated someone to do something. For example, "The success he achieved in his own business motivated us to start our own company."
These two facts motivated us to analyse the widely used AA indices.
These incongruent results motivated us to examine the topic.
This result motivated us to study IRI performance throughout protracted solar minimum of the 24th cycle.
This has motivated us to propose a new lightweight scheme to rectify the problem.
The formula (2.17) motivated us to observe the following theorem.
This need motivated us to perform our study.
This fact motivated us to observe the following theorem.
These motivated us to work on the present topic.
This result motivated us to further study the initial points.
These considerations have motivated us to consider the following problem.
The above example motivated us to define the following.
I love the desktop app, it’s always running on my Mac. Ludwig is the best English buddy, it answers my 100 queries per day and stays cool.
Cristina Valenza
Retail Lead Linguist @ Apple Inc.