The English word “encourage” has three distinct meanings:
1) to help someone to have a more positive outlook
2) to use words to persuade a person to take some specific action
3) to create a favorable environment for some activity or behavior, without necessarily intending to do so
For example, if a friend has been sick lately and is feeling sad, we might pay a visit to encourage him. If our words help him to have a less negative view and feel more able to deal with life, we have encouraged him in the first sense.
Another friend may have lost his job. We see an advertisement and encourage him to apply. Since we are urging him to act, we are encouraging him in the second sense.
As an example of the third meaning, government grants may be intended to encourage small business. A poorly thought out policy may encourage corruption. A lack of hand washing facilities may encourage the spread of disease.
So we have three very different circumstances in which English speakers living long ago saw a question of courage. But there are many other ways of looking at these situations, so there is no reasons to assume that Russian speakers chose the same metaphor or even a single metaphor for all three. As we see below, they chose two basic concepts: wakefulness and reward.
This literally means to help a person to be fully awake and alert. Use it to talk about improving your sick friend’s mood:
Мы пошли ободрять подавленного друга.
We went to encourage our depressed friend.
Never use ободрать to say that an action was encouraged. This does not make sense:
Мы ободрили его пожертвовать добродетельным организациям. INCORRECT
We cheered him up to contribute to charity.
Literally, to attempt to awaken someone from sleep. Use this when an action is strongly suggested.
Он побуждал меня подать заявку.
He was encouraging me to put in an application.
To offer cooperation, sympathy, or reward to those who behave in a certain way. Use it to talk about the creation of an atmosphere in which approved behaviors are encouraged. For example:
Этой новой политикой государство поощряет брать большее людей на работу.
With this new policy the government is encouraging hiring.
Не надо его поощрять.
You shouldn’t be encouraging him.