
animieren zu
to encourage to
To encourage, motivate, or prompt someone to do something specific.
Die gute Musik animierte die Gäste zum Tanzen.
The good music encouraged the guests to dance.
to encourage / animate
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to encourage to
To encourage, motivate, or prompt someone to do something specific.
Die gute Musik animierte die Gäste zum Tanzen.
The good music encouraged the guests to dance.

to animate
To technically process images or figures so that the impression of movement is created, as in a cartoon or computer-animated film.
Es dauert Monate, eine einzige Figur für einen Kinofilm zu animieren.
It takes months to animate a single character for a feature film.

to entertain
To entertain guests as an activity leader or entertainer (e.g., in a hotel or club) and encourage them to take part in activities.
Der Animateur versucht, die Hotelgäste für Wassergymnastik zu animieren.
The entertainer tries to encourage the hotel guests to join in water aerobics.
Like many verbs ending in '-ieren', 'animieren' (to encourage / animate) comes from another language and is conjugated regularly. The past participle is formed without 'ge-': animiert.
Er hat die Zeichnungen für den Kurzfilm selbst animiert.
He animated the drawings for the short film himself.
You can tell which meaning is intended from the object and context. If you 'animiert' a person 'zu' something, it means 'to encourage'. If you animate a figure or an image, it is about animation techniques. If you entertain guests, it is about holiday entertainment.
Die Werbung soll die Leute zum Kaufen animieren.
The advertisement is meant to encourage people to buy.
In the meaning 'ermutigen' (to encourage), 'animieren' is almost always used with the preposition 'zu' and the dative. You encourage someone to do an activity or adopt a behavior.
Der Trainer animierte die Mannschaft zu mehr Einsatz.
The coach encouraged the team to show more commitment.
The meaning of entertaining guests is typical in the area of tourism and leisure. A person who does this professionally is called an 'Animateur' or 'Animateurin' (entertainer/activity leader).
Im Clubhotel werden die Urlauber den ganzen Tag animiert, bei Spielen mitzumachen.
At the club hotel, holidaymakers are encouraged all day long to join in games.
to move
Both bewegen and animieren can mean getting someone to take an action. Bewegen emphasizes that conviction or influence leads to the decision. Animieren more strongly highlights that someone is encouraged, prompted, or activated.

Mit ihrer Begeisterung animierte sie ihren Bruder dazu, am Kurs teilzunehmen.
Her enthusiasm encouraged her brother to take part in the course.
Nach einem langen Gespräch bewegte sie ihren Bruder dazu, am Kurs teilzunehmen.
After a long conversation, she moved her brother to take part in the course.