Learn Hardcore German: Nach der Übung richte ich meinen Rücken auf.

die Übung = nominative singular (the exercise)
In the dative singular, feminine die becomes der:
- nach der Übung = after the exercise

So the pattern is:
nach + dative → nach dem Essen, nach der Schule, nach der Übung, etc.

What does „Übung“ mean here? Is it physical exercise, or practice like homework?

Übung is fairly broad and can mean:

practice / exercise in a learning context:
- die Grammatikübung – grammar exercise
- Übungen im Buch – exercises in the book
exercise / drill / routine in a physical or sports context:
- Gymnastikübungen – gymnastic exercises
- Dehnübungen – stretching exercises

In this sentence, because of straightening my back, it most naturally suggests a physical exercise or workout-type activity, but context could tip it either way.

If you want to be clearly sporty/fitness-related, many speakers would say „Nach dem Training…“ or „Nach dem Workout…“.

Why is the word order „richte ich“ and not „ich richte“ after „Nach der Übung“?

German main clauses obey the verb-second (V2) rule: the conjugated verb must be in position 2, no matter what comes first.

In a “neutral” sentence:

Ich richte meinen Rücken auf.
Ich is in position 1, so richte is in position 2.

If you move Nach der Übung to the front for emphasis:

Nach der Übung = first element
The verb must still be second → richte
The subject comes after the verb → ich

So you get:

Nach der Übung richte ich meinen Rücken auf.

This inversion (verb before subject) is normal German when you start the sentence with something other than the subject.

Why is „auf“ at the end? What is the infinitive of this verb?

The infinitive is aufrichten – a separable-prefix verb:

Prefix: auf-
Main verb: richten

In a main clause in the present or simple past, separable verbs split:

Ich richte meinen Rücken auf.
Nach der Übung richte ich meinen Rücken auf.

The conjugated part (richte) goes in verb-second position; the prefix auf goes to the end of the clause.

If the verb is in infinitive or past participle form (e.g. with zu, haben, werden), it’s written together again:

… meinen Rücken aufzurichten (infinitive with zu)
Ich habe meinen Rücken aufgerichtet. (perfect)

Why is it „meinen Rücken“ and not „mein Rücken“?

Because Rücken is:

Masculine (der Rücken)
In the accusative case as the direct object

The possessive mein must be declined like an adjective:

Nominative masculine: mein Rücken
Accusative masculine: meinen Rücken

Compare:

Mein Rücken tut weh. – My back hurts. (subject → nominative)
Ich richte meinen Rücken auf. – I straighten my back. (direct object → accusative)

Why is „Rücken“ in the accusative case here?

Because „meinen Rücken“ is the direct object of the verb (auf)richten.

Ask: What do I straighten? → meinen Rücken

In German, the direct object of most action verbs is put into the accusative:

Ich lese ein Buch. – ein Buch = accusative
Ich trinke einen Kaffee. – einen Kaffee = accusative
Ich richte meinen Rücken auf. – meinen Rücken = accusative

Can I say „Ich richte mich auf“ instead? What’s the difference from „Ich richte meinen Rücken auf“?

Both are possible, but the nuance changes:

Ich richte mich auf.
- Literally: I straighten myself up / I sit or stand up straight.
- reflexive: the object is mich, referring to your whole body.
- Natural if you mean I sit up / I stand up straighter.
Ich richte meinen Rücken auf.
- Literally: I straighten my back.
- Focuses specifically on the back as a body part.
- Often used when you are consciously correcting your posture.

So if the goal is “posture correction of the back”, meinen Rücken aufrichten is more explicit. For just sitting up or standing up, mich aufrichten is more general.

Where else could I put „nach der Übung“ in the sentence, and does the meaning change?

All of these are grammatical and mean essentially the same thing; the difference is in emphasis:

Nach der Übung richte ich meinen Rücken auf.
Emphasis on when it happens (after the exercise).
Ich richte nach der Übung meinen Rücken auf.
Slight emphasis stays on ich richte meinen Rücken auf, with “nach der Übung” inserted.
Ich richte meinen Rücken nach der Übung auf.
Also fine; Germans often put temporal phrases before the separable prefix at the end.

In all versions, nach der Übung refers to the time of the action. The main word-order rule that never changes: the finite verb stays second (in main clauses).

Can this present-tense sentence also mean “After the exercise, I will straighten my back” in German?

Yes. German Präsens often covers both:

present meaning: After the exercise, I straighten my back (that’s my routine).
future meaning: After the exercise, I’ll straighten my back. (plan / scheduled action)

Whether it’s present or future is usually clear from context. If you really want to stress the future, you can use Futur I:

Nach der Übung werde ich meinen Rücken aufrichten.
(After the exercise, I will straighten my back.)

But in everyday speech, the simple present you have is more common.

What’s the difference between „Nach der Übung“ and „Nach dem Training“?

Both can be used, but they have slightly different flavor:

Übung
- Very general: exercise, practice, drill, task.
- Can be a single exercise in a workout, or a practice activity in many contexts (music, language, etc.).
Training
- More strongly associated with sports / workouts / athletic practice.
- Sounds more like a whole training session.

So:

Nach der Übung richte ich meinen Rücken auf.
- Could refer to one exercise (e.g. after one particular drill or stretch).
Nach dem Training richte ich meinen Rücken auf.
- Suggests after the whole workout / training session.

Context will make it clear what you mean.

Can I say „Danach richte ich meinen Rücken auf.“ instead of „Nach der Übung…“? What’s the difference?

Yes, you can.

Nach der Übung…
- Literally: After the exercise…
- Specifies what comes before (the exercise).
Danach…
- Literally: Afterwards / after that…
- Refers back to something just mentioned in the previous context.

You’d use danach if it’s clear from the previous sentence what “that” is:

Ich mache eine Übung. Danach richte ich meinen Rücken auf.

If you’re starting a conversation or want to be explicit without earlier context, Nach der Übung… is clearer.

How would this sentence look in the past tense?

Most commonly you’ll use the Perfekt (spoken past):

Nach der Übung habe ich meinen Rücken aufgerichtet.
(After the exercise, I straightened my back.)

Structure:

Auxiliary haben in second position: habe
Past participle of aufrichten at the end: aufgerichtet

In Präteritum (simple past), which is less common in everyday speech but fine in writing:

Nach der Übung richtete ich meinen Rücken auf.

Here, richtete is the simple past form; because it’s a separable verb in the present, its simple past keeps the prefix attached only in the infinitive and past participle, but in the finite Präteritum form it appears as richtete … auf in normal usage:

More natural: Nach der Übung richtete ich meinen Rücken auf.
(finite verb second, prefix at the end, like in the present)
Past participle form together: aufgerichtet (used only with haben).