Are the words "mandatory," "obligatory," and "compulsory" interchangeable?

As a non-native speaker, I wonder what the rules are for preferring one of "mandatory", "obligatory" or "compulsory" over the others.

The Corpus of Contemporary American English yields examples such as these:

Mandatory: 4865 cases

• mandatory safety nets around trampolines


• mandatory health care reform


• mandatory sentence for first-degree murder


• Unemployment sent me a letter, said this was a mandatory class.


• To stave off matting, daily brushing with a paddle brush is mandatory.


• He believes he can fill the role of rangy wing scorer that seems almost mandatory for championship teams.


• "Self-deprecation is mandatory here", he said.

Compulsory: 1060 cases

• compulsory health insurance


• states that prohibit compulsory unionism


• compulsory celibacy for the clergy


• added to the school curriculum as a compulsory second language


• U.S. imperialism can be thought of as a system of compulsory heterosexuality


• My landlord and mother made my weekly visits to the center compulsory if I was to continue running my business rent free from her basement.

Obligatory: 808 cases

• the obligatory happy ending


• when the obligatory compliments were out of the way


• I would hang up on my father after the obligatory five minutes


• the laptop computer has become nearly obligatory on campus

"Mandatory" is presumably related to "mandate" and used when it's a matter of law or regulation.

"Obligatory" is presumably related to "obligation" and used when it's a matter of moral, social or other obligation rather than law. (Like "the obligatory happy ending".)

"Compulsory" seems to mean that you are forced to do something, but the forcing mechanism is unspecified?

Is this approximately correct, and are there other rules of thumb for when to use which term?

There seems to be some cases where the terms are interchangeable: "Mandatory health insurance" and "compulsory health insurance" would be equally acceptable, wouldn't it?

Would "school curriculum compulsory second language" read the same if we substitute "mandatory" or "obligatory"?

Answer

I think you mostly have it right, but for further exemplification, here are the most common immediately following collocates for each these words from the COCA:

Most common collocates for mandatory

1   TESTING      151   
2   MINIMUM      125   
3   RETIREMENT   107   
4   MINIMUMS     100   
5   REPORTING    87    
6   SENTENCES    78    
7   EVACUATION   74    
8   SENTENCING   74    
9   DISCLOSURE   63    
10  ARBITRATION  56    
11  SPENDING     41    
12  DRUG         36    
13  SENTENCE     35    
14  EVACUATIONS  32    
15  ARREST       27    
16  PRISON       27    
17  COUNSELING   26    
18  OVERTIME     24    
19  RECYCLING    23    
20  BUSING       22    
21  SANCTIONS    22    
22  INSURANCE    21    
23  SERVICE      21    
24  HIV          20    
25  RELEASE      20    

Most common collocates for compulsory

1   EDUCATION       86
2   MILITARY        53
3   SCHOOL          31
4   SCHOOLING       21
5   STERILIZATION   19
6   LICENSING       18
7   ATTENDANCE      18
8   NATIONAL        16
9   SERVICE         15
10  MILITIA         14
11  MEMBERSHIP      14
12  JURISDICTION    11
13  HEALTH          11
14  HETEROSEXUALITY 10
15  LABOR           10
16  ARBITRATION     9 
17  LICENSE         9 
18  FIGURES         9 
19  PROCESS         9 
20  PUBLIC          9 
21  RETIREMENT      8 
22  DISPUTE         7 
23  ARMY            7 
24  VOTING          6 
25  INSURANCE       6 

Most common collocates for obligatory

1   SERVICE          10 
2   NATURE           8  
3   STOP             8  
4   REFERENCE        6  
5   STRUCTURE        5  
6   CELIBACY         4  
7   EXCHANGE         4  
8   VISIT            4  
9   READING          4  
10  MILITARY         4  
11  QUESTION         4  
12  SLAP             3  
13  NOD              3  
14  RETURNS          3  
15  BASIC            3  
16  PERIOD           3  
17  UPON             3  
18  PHOTO            3  
19  BOOK             3  
20  EARLY            3  
21  PARTHENOGENESIS  2  
22  PREPOSITION      2  
23  PILGRIMAGES      2  
24  HAGGLING         2  
25  ALTRUISTIC       2  

As you can see, mandatory and compulsory have much stronger collocates. The collocates for mandatory are more things that are simply required by law, policy, or rule, whereas compulsory is more for specifically things that someone must do (e.g. education, military, sterilization). Obligatory, on the other hand, doesn’t have much of a strong affinity for certain things, and can be used generally for anything that is required by social custom.